A131321 Triangle read by rows: A168561^2.

1, 0, 1, 2, 0, 1, 0, 4, 0, 1, 5, 0, 6, 0, 1, 0, 14, 0, 8, 0, 1, 13, 0, 27, 0, 10, 0, 1, 0, 46, 0, 44, 0, 12, 0, 1, 34, 0, 107, 0, 65, 0, 14, 0, 1, 0, 145, 0, 204, 0, 90, 0, 16, 0, 1, 89, 0, 393, 0, 345, 0, 119, 0, 18, 0, 1, 0, 444, 0, 854, 0, 538, 0, 152, 0, 20, 0, 1

Offset: 0

Author

Gary W. Adamson, Jun 28 2007

Keywords

• nonn
• tabl

Comments

Left border, nonzero terms = odd indexed Fibonacci numbers: (1, 2, 5, 13, ...). Next column, nonzero terms = A030267: (1, 4, 14, 46, 145, ...). Row sums = A131322: (1, 1, 3, 5, 12, 23, 51, ...).

Riordan array (f(x),x*f(x)) where f(x) = (1-x^2)/(1-3*x^2+x^4). Aerated version of triangle in A188137. - Philippe Deléham, Jan 26 2012

Examples

			First few rows of the triangle are:
   1;
   0,  1;
   2,  0,  1;
   0,  4,  0,  1;
   5,  0,  6,  0,  1;
   0, 14,  0,  8,  0,  1;
  13,  0, 27,  0, 10,  0,  1;
  ...
		

Crossrefs

Cf. A049310, A030267, A168561, A188137.

Programs

Maple

F:= (n, k)-> coeff(combinat[fibonacci](n+1, x), x, k):
T:= (n, k)-> add(F(n, j)*F(j, k), j=0..n):
seq(seq(T(n, k), k=0..n), n=0..14);  # Alois P. Heinz, Dec 12 2019

Formula

A168561 squared, as an infinite lower triangular matrix.