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%I #5 Mar 30 2012 18:51:58
%S 0,0,1,-1,0,1,-3,2,1,-5,8,-4,-7,18,-20,9,32,-56,49,-25,-120,161,-123,
%T 82,401,-445,328,-284,-1247,1218,-940,969,3712,-3376,2849,-3185,
%U -10800,9601,-8883,10082,31201,-28085,27848,-30964,-90487,84018,-86660,93129,264992,-254696
%N Table T(n,k)= -2T(n-1,k)+T(n-1,k+1) = T(n,k-4), 0<=n.
%C 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 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 T(n,k) = T(n,k-1)+T(n,k-2)+T(n,k-3)+2T(n,k-4).
%F Row sums are sum_{k=1..4) T(n,k) = 0.
%F Row sums of absolute values: sum_{k=1..4} |T(n,k)| = A008776(n).
%F A140289(n)=T(n,1). A140290(n)=T(n,4).
%e The table starts
%e 0, 0, 1,-1, 0, 0, 1,-1,...
%e 0, 1, -3, 2, 0, 1, -3, 2,...
%e 1,-5, 8,-4, 1,-5, 8,-4,...
%e -7,18,-20, 9,-7,18,-20, 9,...
%e and only the first 4 columns (the non-redundant information) build the sequence.
%K sign,tabf,less
%O 0,7
%A _Paul Curtz_, May 24 2008
%E Edited and extended by _R. J. Mathar_, Jul 22 2008
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