PostgreSQL sequence based on another column

No problem! We're going to make two tables, things and stuff. stuff will be the table you describe in your question, and things is the one it refers to:

CREATE TABLE things (
    id serial primary key,
    name text
);

CREATE TABLE stuff (
    id integer references things,
    seq integer NOT NULL,
    notes text,
    primary key (id, seq)
);

Then we'll set things up with a trigger that will create a new sequence every time a row is created:

CREATE FUNCTION make_thing_seq() RETURNS trigger
    LANGUAGE plpgsql
    AS $$
begin
  execute format('create sequence thing_seq_%s', NEW.id);
  return NEW;
end
$$;

CREATE TRIGGER make_thing_seq AFTER INSERT ON things FOR EACH ROW EXECUTE PROCEDURE make_thing_seq();

Now we'll end up with thing_seq_1, thing_seq_2, etc, etc...

Now another trigger on stuff so that it uses the right sequence each time:

CREATE FUNCTION fill_in_stuff_seq() RETURNS trigger
    LANGUAGE plpgsql
    AS $$
begin
  NEW.seq := nextval('thing_seq_' || NEW.id);
  RETURN NEW;
end
$$;

CREATE TRIGGER fill_in_stuff_seq BEFORE INSERT ON stuff FOR EACH ROW EXECUTE PROCEDURE fill_in_stuff_seq();

That'll ensure that when rows go into stuff, the id column is used to find the right sequence to call nextval on.

Here's a demonstration:

test=# insert into things (name) values ('Joe');
INSERT 0 1
test=# insert into things (name) values ('Bob');
INSERT 0 1
test=# select * from things;
 id | name
----+------
  1 | Joe
  2 | Bob
(2 rows)

test=# \d
              List of relations
 Schema |     Name      |   Type   |  Owner
--------+---------------+----------+----------
 public | stuff         | table    | jkominek
 public | thing_seq_1   | sequence | jkominek
 public | thing_seq_2   | sequence | jkominek
 public | things        | table    | jkominek
 public | things_id_seq | sequence | jkominek
(5 rows)

test=# insert into stuff (id, notes) values (1, 'Keychain');
INSERT 0 1
test=# insert into stuff (id, notes) values (1, 'Pet goat');
INSERT 0 1
test=# insert into stuff (id, notes) values (2, 'Family photo');
INSERT 0 1
test=# insert into stuff (id, notes) values (1, 'Redundant lawnmower');
INSERT 0 1
test=# select * from stuff;
 id | seq |        notes
----+-----+---------------------
  1 |   1 | Keychain
  1 |   2 | Pet goat
  2 |   1 | Family photo
  1 |   3 | Redundant lawnmower
(4 rows)

test=#

You could use a window function to assign your SEQ values, something like:

INSERT INTO YourTable
    (ID, SEQ, DATA)
    SELECT ID, ROW_NUMBER() OVER(PARTITION BY ID ORDER BY DATA), DATA
        FROM YourSource

If seq reflects (or should reflect) the order in which the rows are inserted, I'd rather use a timestamp that gets populated automatically and generate the sequence number on the fly when selecting the rows using row_number():

create table some_table
( 
  id          integer   not null,
  inserted_at timestamp not null default current_timestamp,
  data text
);

The to get the seq column, you can do:

select id,  
       row_number() over (partition by id order by inserted_at) as seq,
       data
from some_table
order by id, seq;

The select is however going to be a bit slower compared to using a persisted seq column (especially with an index on id, seq).

If that becomes a problem you can either look into using a materialized view, or adding the seq column and then updating it on a regular basis (I would not do this in a trigger for performance reasons).

SQLFiddle example: http://sqlfiddle.com/#!15/db69b/1

Just a guess.

INSERT INTO TABLE (ID, SEQ, DATA)
VALUES
(
 IDVALUE,
 (SELECT max(SEQ) +1 FROM TABLE WHERE ID = IDVALUU),
 DATAVALUE
);

Here's a simple way using standard SQL:

INSERT INTO mytable (id, seq, data)
SELECT << your desired ID >>,
       COUNT(*) + 1,
       'Quick brown fox, lorem ipsum, lazy dog, etc etc.'
FROM mytable
WHERE id = << your desired ID (same as above) >>;

See SQL Fiddle Demo.

(If you wanted to be a bit cleverer you could consider creating a trigger to update the row using the same method immediately after an insert.)

I had the same need to dynamicaly store a tree-like structure, not to add all IDs at once.
I prefer not use sequence table for each group as there could be thousands of them.
It run in an intensive multi-processing environment, so it has to be race-condition-proof.
Here the insert fonction for the 1st level. Other levels follow the same principle.

Each group as independent non-reusable sequencial IDs, the function receives a group name & sub-group name, gives you the existing ID or creates it & returns the new ID.
I tried a loop to have a single select, but the code is as long & harder to read.

CREATE OR REPLACE FUNCTION getOrInsert(myGroupName TEXT, mySubGroupName TEXT)
  RETURNS INT AS
$BODY$
DECLARE
   myId INT;
BEGIN -- 1st try to get it if it already exists
   SELECT id INTO myId FROM myTable
      WHERE groupName=myGroupName AND subGroupName=mySubGroupName;
   IF NOT FOUND THEN
      -- Only 1 session can get it but others can read
      LOCK TABLE myTable IN SHARE ROW EXCLUSIVE MODE; 
      -- 2nd try in case of race condition
      SELECT id INTO myId FROM myTable
         WHERE groupName=myGroupName AND subGroupName=mySubGroupName;
      IF NOT FOUND THEN -- Doesn't exist. Get next ID for this group.
         SELECT COALESCE(MAX(id), 0)+1 INTO myId FROM myTable
            WHERE groupName=myGroupName;
         INSERT INTO myTable (groupName, id, subGroupName)
            VALUES (myGroupName, myId, mySubGroupName);
      END IF;
   END IF;
   RETURN myId;
END;
$BODY$
  LANGUAGE plpgsql VOLATILE COST 100;

To try it:

CREATE TABLE myTable (GroupName TEXT, SubGroupName TEXT, id INT);
SELECT getOrInsert('groupA', 'subgroupX'); -- Returns 1
...
SELECT * FROM myTable;
 groupname | subgroupname | id 
-----------+--------------+----
 groupA    | subgroupX    |  1
 groupA    | subgroupY    |  2
 groupA    | subgroupZ    |  3
 groupB    | subgroupY    |  1