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

Author

Gary W. Adamson, Nov 05 2008

Keywords

• nonn
• tabl

Comments

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

Examples

			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.

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.