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%I #4 Oct 30 2022 21:20:56
%S 1,-1,1,0,0,1,0,0,0,1,1,-1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,-1,0,0,
%T 0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,0,0,0,0,1,0,
%U 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Inverse of matrix (1,x)+(x,x^3).
%C Row sums are A014578(n+5) or sum{k=0..ceiling(log(n+4)/log(3)),(-1)^k*(floor((n+4)/3^k)-floor((n+3)/3^k)}. Inverse of number triangle A115512.
%e Triangle begins
%e 1,
%e -1, 1,
%e 0, 0, 1,
%e 0, 0, 0, 1,
%e 1, -1, 0, 0, 1,
%e 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, -1, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
%Y Cf. A014578, A115512.
%K sign,tabl
%O 0,1
%A _Paul Barry_, Jan 23 2006
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