A220693 Irregular triangle where the k-th item in the n-th row (both starting from 1) tells in how many ways we can add 2 distinct integers from 1 to n in such a way that the sum is divisible by k. Row n has 2n-1 terms.

0, 1, 0, 1, 3, 1, 1, 1, 1, 6, 2, 2, 1, 2, 1, 1, 10, 4, 4, 2, 2, 2, 2, 1, 1, 15, 6, 5, 3, 3, 2, 3, 2, 2, 1, 1, 21, 9, 7, 5, 4, 3, 3, 3, 3, 2, 2, 1, 1, 28, 12, 10, 6, 6, 4, 4, 3, 4, 3, 3, 2, 2, 1, 1, 36, 16, 12, 8, 8, 5, 5, 4, 4, 4, 4, 3, 3, 2, 2, 1, 1

Offset: 1

Author

Antti Karttunen, Feb 18 2013. Proposed by Robert Israel, May 07 2012

Keywords

• nonn
• tabf

Comments

After the first two rows, this irregular table gives all the nonzero terms from the beginning of each row of A220691. See the comments there and at A061857.

Examples

			Row n (starting from row 1) has 2n-1 terms in this irregular table:
   0;
   1, 0, 1;
   3, 1, 1, 1, 1;
   6, 2, 2, 1, 2, 1, 1;
  10, 4, 4, 2, 2, 2, 2, 1, 1;
  15, 6, 5, 3, 3, 2, 3, 2, 2, 1, 1;
  etc.
See A220691 and A061857 for the meaning of each term.
		

Links

• Antti Karttunen, Rows n = 1..100 of table, flattened
• Index entries for sequences related to subset sums modulo m

Programs

Scheme

(define (A220693 n) (A220691bi (A003059 n) (A071797 n)))
;; For A220691bi see A220691.

Formula

See Robert Israel's formula at A061857.