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A168260 Triangle read by rows, A168258 * the diagonalized variant of A168259.

%I A168260 #9 Nov 19 2022 15:55:54
%S A168260 1,1,1,2,2,2,2,2,4,6,3,3,6,12,14,3,3,6,18,28,38,4,4,8,24,42,76,96,4,4,
%T A168260 8,24,56,114,192,254,5,5,10,30,70,152,288,508,656,5,5,10,30,70,190,
%U A168260 384,762,1312,1724,6,6,12,36,84,228,480,1016
%N A168260 Triangle read by rows, A168258 * the diagonalized variant of A168259.
%C A168260 Row sums = A168259: (1, 2, 6, 14, 38, 96, ...).
%C A168260 Sum of n-th row terms = rightmost term of next row.
%C A168260 Conjecture: Row sum ratios tend to phi^2 = 2.6180339... (cf. A168259).
%F A168260 Let M = triangle A168258 and Q = the diagonalized variant of M's eigensequence
%F A168260 such that Q's rightmost diagonal = A168259 prefaced with a 1: (1, 1, 2, 6, ...).
%F A168260 and other terms = 0.
%F A168260 Triangle A168260 = M * Q as infinite lower triangular matrices.
%e A168260 Triangle begins:
%e A168260   1;
%e A168260   1, 1;
%e A168260   2, 2,  2;
%e A168260   2, 2,  4,  6;
%e A168260   3, 3,  6, 12,  14;
%e A168260   3, 3,  6, 18,  28,  38;
%e A168260   4, 4,  8, 24,  42,  76,  96;
%e A168260   4, 4,  8, 24,  56, 114, 192,  254;
%e A168260   5, 5, 10, 30,  70, 152, 288,  508,  656;
%e A168260   5, 5, 10, 30,  70, 190, 384,  762, 1312,  1724;
%e A168260   6, 6, 12, 36,  84, 228, 480, 1016, 1968,  3448,  4492;
%e A168260   6, 6, 12, 36,  84, 228, 576, 1270, 2624,  5172,  8984, 11776;
%e A168260   7, 7, 14, 42,  98, 266, 672, 1524, 3284,  6896, 13476, 23552,  30774;
%e A168260   7, 7, 14, 42,  98, 266, 672, 1778, 3936,  8620, 17968, 35328,  61548,  80608;
%e A168260   8, 8, 16, 48, 112, 304, 768, 2032, 5248, 12068, 26952, 58880, 123096, 241824;
%e A168260   ...
%Y A168260 Cf. A168258, A168259.
%K A168260 nonn,tabl
%O A168260 1,4
%A A168260 _Gary W. Adamson_, Nov 21 2009