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.

A110515 Sequence array for (1 - x + x^2 + x^3)/(1 - x^4).

This page as a plain text file.
%I A110515 #9 Aug 29 2017 22:51:22
%S A110515 1,-1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,
%T A110515 -1,1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,1,
%U A110515 -1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1
%N A110515 Sequence array for (1 - x + x^2 + x^3)/(1 - x^4).
%C A110515 Row sums are A106249. Diagonal sums are A110514.
%H A110515 G. C. Greubel, <a href="/A110515/b110515.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A110515 Riordan array ((1 - x + x^2 + x^3)/(1 - x^4), 1).
%F A110515 Column k has g.f. x^k*(1 - x + x^2 + x^3)/(1 - x^4).
%F A110515 T(n, k) = if(k <= n, -sin(Pi*(n-k)/2) + cos(Pi*(n-k))/2 + 1/2, 0).
%F A110515 T(n, k) = if(k <= n, Jacobi(2^(n-k), 2(n-k)+1), 0) [conjecture].
%e A110515 Rows begin
%e A110515    1;
%e A110515   -1,  1;
%e A110515    1, -1,  1;
%e A110515    1,  1, -1,  1;
%e A110515    1,  1,  1, -1,  1;
%e A110515   -1,  1,  1,  1, -1,  1;
%e A110515    1, -1,  1,  1,  1,- 1,  1;
%t A110515 Table[If[k <= n, -Sin[Pi*(n - k)/2] + Cos[Pi*(n - k)]/2 + 1/2, 0], {n,0, 10}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Aug 29 2017 *)
%o A110515 (PARI) for(n=0,20, for(k=0,n, print1(round(if(k<=n, -sin(Pi*(n-k)/2) + cos(Pi*(n-k))/2 + 1/2, 0)), ", "))) \\ _G. C. Greubel_, Aug 29 2017
%K A110515 easy,sign,tabl
%O A110515 0,1
%A A110515 _Paul Barry_, Jul 24 2005