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

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, 8, 24, 56, 114, 192, 254, 5, 5, 10, 30, 70, 152, 288, 508, 656, 5, 5, 10, 30, 70, 190, 384, 762, 1312, 1724, 6, 6, 12, 36, 84, 228, 480, 1016

Offset: 1

Author

Gary W. Adamson, Nov 21 2009

Keywords

• nonn
• tabl

Comments

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

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

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

Examples

			Triangle begins:
  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,  8, 24,  56, 114, 192,  254;
  5, 5, 10, 30,  70, 152, 288,  508,  656;
  5, 5, 10, 30,  70, 190, 384,  762, 1312,  1724;
  6, 6, 12, 36,  84, 228, 480, 1016, 1968,  3448,  4492;
  6, 6, 12, 36,  84, 228, 576, 1270, 2624,  5172,  8984, 11776;
  7, 7, 14, 42,  98, 266, 672, 1524, 3284,  6896, 13476, 23552,  30774;
  7, 7, 14, 42,  98, 266, 672, 1778, 3936,  8620, 17968, 35328,  61548,  80608;
  8, 8, 16, 48, 112, 304, 768, 2032, 5248, 12068, 26952, 58880, 123096, 241824;
  ...
		

Crossrefs

Cf. A168258, A168259.

Formula

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

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

and other terms = 0.

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