A092422 Triangle, read by rows, where T(n,k) equals the k-th term of the convolution of the (n-k)-th row with the (2k)-th Fibonacci polynomial (A011973).

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 8, 7, 1, 1, 5, 14, 18, 11, 1, 1, 6, 21, 40, 36, 16, 1, 1, 7, 30, 72, 98, 66, 22, 1, 1, 8, 40, 119, 211, 214, 113, 29, 1, 1, 9, 52, 182, 398, 546, 428, 183, 37, 1, 1, 10, 65, 265, 692, 1170, 1278, 799, 283, 46, 1, 1, 11, 80, 368, 1123, 2286, 3104

Offset: 0

Author

Paul D. Hanna, Mar 22 2004

Keywords

• nonn
• tabl

Examples

			Even-numbered Fibonacci polynomials (cf. A011973) are:
{1},
{1,1},
{1,3,1},
{1,5,6,1},
{1,7,15,10,1},...
These terms are used to generate each row from the prior rows. For example,
row 5 = {1(1), 1(1)+1(4), 1(1)+3(3)+1(4), 1(1)+6(2)+5(1), 1(1)+10(1), 1(1)};
row 6 = {1(1), 1(1)+1(5), 1(1)+3(4)+1(8), 1(1)+6(3)+5(4)+1(1), 1(1)+10(2)+15(1), 1(1)+15(1), 1(1)}.
Rows begin:
{1},
{1,1},
{1,2,1},
{1,3,4,1},
{1,4,8,7,1},
{1,5,14,18,11,1},
{1,6,21,40,36,16,1},
{1,7,30,72,98,66,22,1},
{1,8,40,119,211,214,113,29,1},
{1,9,52,182,398,546,428,183,37,1},...
		

Crossrefs

Cf. A092423, A092424, A011973.

Programs

PARI

T(n,k)=if(n
				

Formula

T(n, k) = sum_{j=0, min(k, n-k)} binomial(k+j, k-j)*T(n-k, j) with T(n, 0)=1.