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.
%I A132780 #10 Jul 06 2019 19:22:45
%S A132780 1,1,1,1,3,7,15,29,57,113,227,455,911,1821,3641,7281,14563,29127,
%T A132780 58255,116509,233017,466033,932067,1864135,3728271,7456541,14913081,
%U A132780 29826161,59652323,119304647,238609295,477218589,954437177,1908874353,3817748707
%N A132780 a(0)=1. a(n+1)=2*a(n)-A130151(n).
%C A132780 The first member of the sequences of the d'-th differences (that is, the diagonal of the pyramidal arrangement of repeated differences and essentially the binomial transform of 2*A113405) has the same absolute value as the first differences themselves, cf. the comment in A113405.
%H A132780 Harvey P. Dale, <a href="/A132780/b132780.txt">Table of n, a(n) for n = 0..1000</a>
%F A132780 First differences: a(n+1)-a(n)= 2*A113405(n).
%F A132780 O.g.f.: (1-x-x^2)/((1+x)(1-x+x^2)(1-2x)). - _R. J. Mathar_, Jul 16 2008
%t A132780 nxt[{n_,a_}]:={n+1,If[MemberQ[{1,2,3},Mod[n+1,6]],2a-1,2a+1]}; NestList[ nxt, {0,1},40][[All,2]] (* _Harvey P. Dale_, Jul 06 2019 *)
%K A132780 nonn
%O A132780 0,5
%A A132780 _Paul Curtz_, Nov 17 2007
%E A132780 Edited and extended by _R. J. Mathar_, Jul 16 2008