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%I #4 Jun 22 2021 14:40:05
%S 1,2,1,2,0,3,2,0,6,5,2,0,6,0,13,2,0,6,0,26,21,2,0,6,0,26,0,55,2,0,6,0,
%T 26,0,110,89,2,0,6,0,26,0,110,0,233,2,0,6,0,26,0,110,0,466,377,1,0,6,
%U 0,26,0,110,0,466,0,987
%N Triangle, row sums = odd Fibonacci numbers, A014437.
%C Row sums = A014437 starting (1, 3, 5, 13, 21, 55, 89, 233, 377,...). The generating triangle M (alternate columns of (1,2,2,2,...) and (1,0,0,0,...) has an eigensequence of (1, 3, 5, 13, 21, 55, 89,...); i.e., the odd Fibonacci numbers; such that M * (1, 1, 3, 5, 13,...) shifts the latter sequence to the left.
%C Sum of n-th row terms = rightmost term of next row.
%F Let M = an infinite lower triangular matrix with alternate columns of
%F (1,2,2,2,...) and (1,0,0,0,...). Let Q = A014437: (1, 1, 3, 5, 13, 21, 55,...);
%F diagonalized with the rest zeros. Triangle A177995 = M * Q.
%e First few rows of the triangle =
%e 1;
%e 2, 1;
%e 2, 0, 3;
%e 2, 0, 6, 5;
%e 2, 0, 6, 0, 13;
%e 2, 0, 6, 0, 26, 21;
%e 2, 0, 6, 0, 26, 0, 55;
%e 2, 0, 6, 0, 26, 0, 110, 89;
%e 2, 0, 6, 0, 26, 0, 110, 0, 233;
%e 2, 0, 6, 0, 26, 0, 110, 0, 466, 377;
%e 2, 0, 6, 0, 26, 0, 110, 0, 466, 0, 987;
%e 2, 0, 6, 0, 26, 0, 110, 0, 466, 0, 1974, 1597;
%e ...
%Y Cf. A014437.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, May 16 2010
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