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 A140287 #10 Sep 29 2024 16:04:04
%S A140287 0,0,1,-1,0,1,-3,2,1,-5,8,-4,-7,18,-20,9,32,-56,49,-25,-120,161,-123,
%T A140287 82,401,-445,328,-284,-1247,1218,-940,969,3712,-3376,2849,-3185,
%U A140287 -10800,9601,-8883,10082,31201,-28085,27848,-30964,-90487,84018,-86660,93129,264992,-254696
%N A140287 Table T(n,k) = -2*T(n-1,k)+T(n-1,k+1) = T(n,k-4), 0<=n.
%C A140287 The table is created from a nucleus (0,0,1,-1) in the upper row, periodic in each row with length 4 and extended downwards to further rows with the Pascal/Galton mixing coefficients (0,-2,1).
%C A140287 Each row may be regarded as coefficients in recurrences of a group of sequences, b_i(n) = Sum_{k=1..4} T(i,k)*b_i(n-k).
%F A140287 T(n,k) = T(n,k-1)+T(n,k-2)+T(n,k-3)+2*T(n,k-4).
%F A140287 Row sums are Sum_{k=1..4} T(n,k) = 0.
%F A140287 Row sums of absolute values: Sum_{k=1..4} |T(n,k)| = A008776(n).
%F A140287 A140289(n)=T(n,1). A140290(n)=T(n,4).
%e A140287 The table starts:
%e A140287 0, 0, 1, -1, 0, 0, 1, -1,...
%e A140287 0, 1, -3, 2, 0, 1, -3, 2,...
%e A140287 1, -5, 8, -4, 1, -5, 8, -4,...
%e A140287 -7, 18, -20, 9, -7, 18, -20, 9,...
%e A140287 and only the first 4 columns (the non-redundant information) build the sequence.
%K A140287 sign,tabf,less
%O A140287 0,7
%A A140287 _Paul Curtz_, May 24 2008
%E A140287 Edited and extended by _R. J. Mathar_, Jul 22 2008