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%I #11 Feb 10 2022 20:30:23
%S 1,1,1,-1,1,2,0,-1,2,2,-1,0,-2,2,3,2,-1,0,-2,3,2,-1,2,-2,0,-3,2,4,-1,
%T -1,4,-2,0,-2,4,2,3,-1,-2,4,-3,0,-4,2,4,-4,3,-2,-2,6,-2,0,-2,4,3,2,-4,
%U 6,-2,-3,4,-4,0,-4,3,4
%N Triangle, row sums = d(n) = A000005(n): M * Q; where M = an infinite lower Toeplitz matrix with A159933 in every column. Q = an infinite lower triangular matrix with d(n) shifted: (1, 1, 2, 2, 3, 2, 4, ...) as the main diagonal and the rest zeros.
%C Triangle = an infinite lower triangular Toeplitz matrix with the INVERTi transform of d(n) in every column; i.e., A159933: (1, 1, -1, 0, -1, 2, -1, ...). Row sums of the resulting eigentriangle of d(n) = d(n).
%C Sum of n-th row terms = rightmost term of next row.
%C Right border = d(n) shifted.
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e -1, 1, 2;
%e 0, -1, 2, 2;
%e -1, 0, -2, 2, 3;
%e 2, -1, 0, -2, 3, 2;
%e -1, 2, -2, 0, -3, 2, 4;
%e -1, -1, 4, -2, 0, -2, 4, 2;
%e 3, -1, -2, 4, -3, 0, -4, 2, 4;
%e -4, 3, -2, -2, 6, -2, 0, -2, 4, 3;
%e 2, -4, 6, -2, -3, 4, -4, 0, -4, 3, 4;
%e 2, 2, -8, 6, -3, -2, 8, -2, 0, -3, 4, 2;
%e -3, 2, 4, -8, 9, -2, -4, 4, -4, 0, -4, 2, 6;
%e 0, -3, 4, 4, -12, 6, -4, -2, 8, -3, 0, -2, 6, 2;
%e 0, 0, -6, 4, 6, -8, 12, -2, -4, 6, -4, 0, -6, 2, 4;
%e 6, 0, 0, -6, 6, 4, -16, 6, -4, -3, 8, -2, 0, -2, 4, 4;
%e ...
%e Example: row 6 = (2, -1, 0, -2, 3, 2) = termwise products of (2, -1, 0, -1, 1, 1) and (1, 1, 2, 2, 3, 2); with dot product sum = 4 = d(6).
%Y Cf. A000005, A159933.
%K tabl,sign
%O 1,6
%A _Gary W. Adamson_, Apr 26 2009
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