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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.

%I A220693 #20 Jul 09 2025 04:35:25
%S A220693 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,
%T A220693 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,
%U A220693 16,12,8,8,5,5,4,4,4,4,3,3,2,2,1,1
%N 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.
%C A220693 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.
%H A220693 Antti Karttunen, <a href="/A220693/b220693.txt">Rows n = 1..100 of table, flattened</a>
%H A220693 <a href="/index/Su#subsetsums">Index entries for sequences related to subset sums modulo m</a>
%F A220693 See _Robert Israel_'s formula at A061857.
%e A220693 Row n (starting from row 1) has 2n-1 terms in this irregular table:
%e A220693    0;
%e A220693    1, 0, 1;
%e A220693    3, 1, 1, 1, 1;
%e A220693    6, 2, 2, 1, 2, 1, 1;
%e A220693   10, 4, 4, 2, 2, 2, 2, 1, 1;
%e A220693   15, 6, 5, 3, 3, 2, 3, 2, 2, 1, 1;
%e A220693   etc.
%e A220693 See A220691 and A061857 for the meaning of each term.
%o A220693 (Scheme) (define (A220693 n) (A220691bi (A003059 n) (A071797 n)))
%o A220693 ;; For A220691bi see A220691.
%K A220693 nonn,tabf
%O A220693 1,5
%A A220693 _Antti Karttunen_, Feb 18 2013. Proposed by _Robert Israel_, May 07 2012