cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A201550 Number of arrays of n integers in -6..6 with sum zero.

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%I A201550 #38 Mar 19 2025 08:07:36
%S A201550 1,1,13,127,1469,17151,204763,2473325,30162301,370487485,4577127763,
%T A201550 56813989827,707972099627,8851373201919,110976634957761,
%U A201550 1394804756117877,17567994350713469,221690794842728445,2802194053806820153
%N A201550 Number of arrays of n integers in -6..6 with sum zero.
%C A201550 Also largest coefficient of (1+x+...+x^12)^n. - _Vaclav Kotesovec_, Aug 09 2013
%H A201550 Seiichi Manyama, <a href="/A201550/b201550.txt">Table of n, a(n) for n = 0..450</a> (terms 1..210 from R. H. Hardin) [It was suggested that the initial terms of this b-file were wrong, but in fact they are correct. - _N. J. A. Sloane_, Jan 19 2019]
%H A201550 Vaclav Kotesovec, <a href="/A201550/a201550.txt">Recurrence</a>
%H A201550 <a href="/index/Ce#cfn">Index entries for sequences of k-nomial coefficients</a>
%F A201550 a(n) ~ 13^n / sqrt(28*Pi*n). - _Vaclav Kotesovec_, Aug 09 2013
%F A201550 a(n) = Sum_{k = 0..floor(n/2)} (-1)^k * binomial(n, k)*binomial(7*n-13*k-1, n-1). - _Peter Bala_, Oct 16 2024
%e A201550 Some solutions for n=5
%e A201550 .-2...-5...-2...-1....3...-6....0...-3....1....6...-6...-2....5....0...-4...-3
%e A201550 ..2...-3...-2....3....0...-1....6...-4....6....1....5....2...-1....3....2....3
%e A201550 ..0...-4....4...-6...-4....1...-3....0...-4...-5....0...-6...-3....0....4...-4
%e A201550 ..0....6....3....5...-5....6....0....4....3...-4....4....0...-5...-3....3...-1
%e A201550 ..0....6...-3...-1....6....0...-3....3...-6....2...-3....6....4....0...-5....5
%p A201550 seq(add((-1)^k * binomial(n, k)*binomial(7*n-13*k-1, n-1), k = 0..floor(n/2)), n = 0..20); # _Peter Bala_, Oct 16 2024
%t A201550 Table[Coefficient[Expand[Sum[x^j,{j,0,12}]^n],x^(6*n)],{n,1,20}] (* _Vaclav Kotesovec_, Aug 09 2013 *)
%o A201550 (PARI) {a(n) = polcoeff((sum(k=0, 12, x^k))^n, 6*n, x)} \\ _Seiichi Manyama_, Dec 14 2018
%Y A201550 Column 6 of A201552. Row 13 of A077042.
%K A201550 nonn,easy
%O A201550 0,3
%A A201550 _R. H. Hardin_, Dec 02 2011
%E A201550 a(0)=1 prepended by _Seiichi Manyama_, Dec 14 2018