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

1,5

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.

Links

Antti Karttunen, Rows n = 1..100 of table, flattened

Index entries for sequences related to subset sums modulo m

Formula

See Robert Israel's formula at A061857.

Example

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.

Prog

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

Crossrefs

Sequence in context: A028264 A208673 A010122 * A208615 A058663 A124371

Adjacent sequences: A220690 A220691 A220692 * A220694 A220695 A220696

Keyword

nonn,tabf

Author

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

Status

approved