A147293 Triangle read by rows, A011782 convolved with A001519.

1, 1, 2, 2, 2, 5, 4, 4, 5, 13, 8, 8, 10, 13, 34, 16, 16, 20, 26, 34, 89, 32, 32, 40, 52, 68, 89, 233, 64, 64, 80, 104, 136, 178, 233, 610, 128, 128, 160, 208, 272, 356, 466, 610, 1597, 256, 256, 320, 416, 544, 712, 932, 1220, 1597, 4181

Offset

0,3

Comments

Row sums = A061667: (1, 3, 9, 26, 73, 201, ...).

Links

Table of n, a(n) for n=0..54.

Formula

Let M = an infinite lower triangular matrix with A011782: (1, 1, 2, 4, 8, 16, ...) in every column; and Q = an infinite lower triangular matrix with odd-indexed Fibonacci numbers, A001519: (1, 2, 5, 13, 34, 89, ...) as the main column and the rest zeros.

A147293 = M * Q.

Example

First few rows of the triangle =
    1;
    1,   2;
    2,   2,   5;
    4,   4,   5,  13;
    8,   8,  10,  13,  34;
   16,  16,  20,  26,  34,  89;
   32,  32,  40,  52,  68,  89, 233;
   64,  64,  80, 104, 136, 178, 233,  610;
  128, 128, 160, 208, 272, 356, 466,  610, 1597;
  256, 256, 320, 416, 544, 712, 932, 1220, 1597, 4181;
  ...
Row 3 = (4, 4, 5, 13) = termwise products of (4, 2, 1, 1) and (1, 2, 5, 13). Row 3 sum of terms = 26 = (1, 1, 2, 4) convolved with (1, 2, 5, 13).

Crossrefs

Cf. A001519, A011782, A061667.

Sequence in context: A209558 A209772 A370164 * A134634 A346500 A103286

Adjacent sequences: A147290 A147291 A147292 * A147294 A147295 A147296

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 05 2008

Status

approved