CREATE TABLE test (
    id INTEGER PRIMARY KEY, 
    some_count INTEGER NOT NULL,
    group_name VARCHAR NOT NULL
);

INSERT INTO test VALUES
    (1, 3, 'a'),
    (2, 2, 'a'),
    (3, 1, 'a'),
    (4, 1, 'a'),
    (5, 1, 'a'),
    (6, 8, 'b'),
    (7, 3, 'b');

WITH RECURSIVE sums (group_name, subset_sum_some_count, max_id, ids) AS (
        SELECT
            group_name, 
            some_count, 
            id,
            array[id] as ids
        FROM test 
        UNION ALL
        SELECT
  	    s.group_name,
            t.some_count + s.subset_sum_some_count,
            t.id,
            array_append(ids, t.id)
        FROM sums s
        JOIN test t ON s.max_id < t.id 
  	WHERE s.subset_sum_some_count <> 3 AND s.group_name = t.group_name 
    )
SELECT DISTINCT ON (group_name) subset_sum_some_count, group_name, ids FROM sums WHERE subset_sum_some_count = 3;