A168260 - OEIS

%I #9 Nov 19 2022 15:55:54

%S 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 8,24,56,114,192,254,5,5,10,30,70,152,288,508,656,5,5,10,30,70,190,

%U 384,762,1312,1724,6,6,12,36,84,228,480,1016

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

%C Row sums = A168259: (1, 2, 6, 14, 38, 96, ...).

%C Sum of n-th row terms = rightmost term of next row.

%C Conjecture: Row sum ratios tend to phi^2 = 2.6180339... (cf. A168259).

%F Let M = triangle A168258 and Q = the diagonalized variant of M's eigensequence

%F such that Q's rightmost diagonal = A168259 prefaced with a 1: (1, 1, 2, 6, ...).

%F and other terms = 0.

%F Triangle A168260 = M * Q as infinite lower triangular matrices.

%e Triangle begins:

%e   1;

%e   1, 1;

%e   2, 2,  2;

%e   2, 2,  4,  6;

%e   3, 3,  6, 12,  14;

%e   3, 3,  6, 18,  28,  38;

%e   4, 4,  8, 24,  42,  76,  96;

%e   4, 4,  8, 24,  56, 114, 192,  254;

%e   5, 5, 10, 30,  70, 152, 288,  508,  656;

%e   5, 5, 10, 30,  70, 190, 384,  762, 1312,  1724;

%e   6, 6, 12, 36,  84, 228, 480, 1016, 1968,  3448,  4492;

%e   6, 6, 12, 36,  84, 228, 576, 1270, 2624,  5172,  8984, 11776;

%e   7, 7, 14, 42,  98, 266, 672, 1524, 3284,  6896, 13476, 23552,  30774;

%e   7, 7, 14, 42,  98, 266, 672, 1778, 3936,  8620, 17968, 35328,  61548,  80608;

%e   8, 8, 16, 48, 112, 304, 768, 2032, 5248, 12068, 26952, 58880, 123096, 241824;

%e   ...

%Y Cf. A168258, A168259.

%K nonn,tabl

%O 1,4

%A _Gary W. Adamson_, Nov 21 2009