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

1,4

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).

Links

Table of n, a(n) for n=1..63.

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.

Example

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.

Sequence in context: A175732 A327817 A353643 * A008737 A244460 A160419

Adjacent sequences: A168257 A168258 A168259 * A168261 A168262 A168263

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 21 2009

Status

approved