A091594 Triangle read by rows: T(n,m) := Sum_{k=0..floor((n-m)/2)} binomial(n-2k,m) * binomial(n-m-k,k).

1, 1, 1, 2, 2, 1, 3, 4, 3, 1, 5, 8, 7, 4, 1, 8, 15, 16, 11, 5, 1, 13, 28, 34, 28, 16, 6, 1, 21, 51, 70, 66, 45, 22, 7, 1, 34, 92, 140, 148, 116, 68, 29, 8, 1, 55, 164, 274, 320, 281, 190, 98, 37, 9, 1, 89, 290, 527, 672, 651, 494, 295, 136, 46, 10, 1, 144, 509, 999, 1379, 1456, 1219, 819, 439, 183, 56, 11, 1

Offset: 0

Author

Paul Barry, Jan 23 2004

Keywords

• easy
• nonn
• tabl

Comments

A Fibonacci related number triangle.

Examples

			Rows begin:
   1,
   1,  1,
   2,  2,  1,
   3,  4,  3,  1,
   5,  8,  7,  4,  1,
   8, 15, 16, 11,  5,  1,
  13, 28, 34, 28, 16,  6, 1,
  21, 51, 70, 66, 45, 22, 7, 1,
  ...
		

Links

• Seiichi Manyama, Rows n = 0..139, flattened

Crossrefs

Columns include A000045, A029907, A054455. Row sums are A006054.

Formula

k-th column has g.f. 1/(1-x-x^2) * ( x*(1-x^2)/(1-x-x^2) )^k.