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

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, 144, 128, 32, 48, 64, 84, 110, 144, 377, 256, 64, 96, 128, 168, 220, 288, 377, 987

Offset

0,2

Comments

Row sums = the even-indexed Fibonacci numbers starting (1, 3, 8, 21, ...).

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, ...).

Row sums of n-th row = rightmost term of next row.

Links

Table of n, a(n) for n=0..44.

Formula

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.

Example

First few rows of the triangle:
    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, 144;
  128,  32,  48,  64,  84, 110, 144, 377;
  256,  64,  96, 128, 168, 220, 288, 377, 987;
  512, 128, 192, 256, 336, 440, 576, 754, 987, 2584;
  ...

Crossrefs

Cf. A137710, A001906.

Sequence in context: A306944 A049776 A286235 * A079276 A210445 A126210

Adjacent sequences: A180336 A180337 A180338 * A180340 A180341 A180342

Keyword

nonn,tabl,more

Author

Gary W. Adamson, Aug 28 2010

Status

approved