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A180339 Triangle by rows, A137710 * a diagonalized variant of A001906.

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%I A180339 #9 Jan 22 2023 09:16:30
%S A180339 1,2,1,4,1,3,8,2,3,8,16,4,6,8,21,32,8,12,16,21,55,64,16,24,32,42,55,
%T A180339 144,128,32,48,64,84,110,144,377,256,64,96,128,168,220,288,377,987
%N A180339 Triangle by rows, A137710 * a diagonalized variant of A001906.
%C A180339 Row sums = the even-indexed Fibonacci numbers starting (1, 3, 8, 21, ...).
%C A180339 Triangle A137710 has (1, 2, 4, 8, 16, ...) as the left border with all other columns = (1, 1, 2, 4, 8, 16,...). The eigensequence of this triangle = the odd-indexed Fibonacci numbers: (1, 3, 8, 21, 55, ...).
%C A180339 Row sums of n-th row = rightmost term of next row.
%F A180339 Let triangle A137710 = M as an infinite lower triangular matrix, with Q = a diagonalized variant of A001906 (1, 1, 3, 8, 21, 55,... as the main diagonal and the rest zeros). This triangle = M*Q.
%e A180339 First few rows of the triangle:
%e A180339     1;
%e A180339     2,   1;
%e A180339     4,   1,   3;
%e A180339     8,   2,   3,   8;
%e A180339    16,   4,   6,   8,  21;
%e A180339    32,   8,  12,  16,  21,  55;
%e A180339    64,  16,  24,  32,  42,  55, 144;
%e A180339   128,  32,  48,  64,  84, 110, 144, 377;
%e A180339   256,  64,  96, 128, 168, 220, 288, 377, 987;
%e A180339   512, 128, 192, 256, 336, 440, 576, 754, 987, 2584;
%e A180339   ...
%Y A180339 Cf. A137710, A001906.
%K A180339 nonn,tabl,more
%O A180339 0,2
%A A180339 _Gary W. Adamson_, Aug 28 2010