A152251 Eigentriangle, row sums = A001519, odd-indexed Fibonacci numbers.

1, 1, 1, 2, 1, 2, 4, 2, 2, 5, 8, 4, 4, 5, 13, 16, 8, 8, 10, 13, 34, 32, 16, 16, 20, 26, 34, 89, 64, 32, 32, 40, 52, 68, 89, 233, 128, 64, 64, 80, 104, 136, 178, 233, 610

Offset: 1

Author

Gary W. Adamson, Nov 30 2008

Keywords

• eigen
• nonn
• tabl

Comments

Row sums = A001519, the odd-indexed Fibonacci numbers starting (1, 2, 5, 13, 34, ...).

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

Examples

			First few rows of the triangle =
    1;
    1,   1;
    2,   1,   2;
    4,   2,   2,   5;
    8,   4,   4,   5,  13;
   16,   8,   8,  10,  13,  34;
   32,  16,  16,  20,  26,  34,  89;
   64,  32,  32,  40,  52,  68,  89, 233;
  128,  64,  64,  80, 104, 136, 178, 233, 610;
  ...
Row 4 = (8, 4, 4, 5, 13) = termwise products of (8, 4, 2, 1, 1) and (1, 1, 2, 5, 13).
		

Crossrefs

Cf. A001519.

Formula

Triangle read by rows, M*Q. M = an infinite lower triangular matrix with (1, 1, 2, 4, 8, 16, ...) in every column and Q = a matrix (1, 1, 2, 5, 13, 34, ...) as the main diagonal and the rest zeros.

Let M = production matrix for reversed rows of the triangle as follows:

1, 1;

1, 0, 2;

1, 0, 0, 2;

1, 0, 0, 0, 2;

1, 0, 0, 0, 0, 2;

...

Reversal of n-th row of triangle A152251 = top row terms of M^(n-1). Example: top row of M^3 = (5, 2, 2, 4). - Gary W. Adamson, Jul 07 2011

Extensions

Last term corrected by Olivier Gérard, Aug 11 2016