A125100 Triangle read by rows: T(n,k) = Fibonacci(k+1)*binomial(n,k) + (k+1)*binomial(n,k+1) (0 <= k <= n).

1, 2, 1, 3, 4, 2, 4, 9, 9, 3, 5, 16, 24, 16, 5, 6, 25, 50, 50, 30, 8, 7, 36, 90, 120, 105, 54, 13, 8, 49, 147, 245, 280, 210, 98, 21, 9, 64, 224, 448, 630, 616, 420, 176, 34, 10, 81, 324, 756, 1260, 1512, 1344, 828, 315, 55, 11, 100, 450, 1200, 2310, 3276, 3570, 2880, 1620

Offset: 0

Author

Gary W. Adamson, Nov 20 2006

Keywords

• nonn
• tabl

Comments

Binomial transform of the bidiagonal matrix with the Fibonacci numbers (1, 1, 2, 3, 5, 8, ...) in the main diagonal and (1, 2, 3, ...) in the subdiagonal.

Sum of terms in row n = n*2^(n-1) + Fibonacci(2n+1) (A081663).

Examples

			First few rows of the triangle:
  1;
  2,   1;
  3,   4,   2;
  4,   9,   9,   3;
  5,  16,  24,  16,   5;
  6,  25,  50,  50,  30,   8;
  7,  36,  90, 120, 105,  54,  13;
  8,  49, 147, 245, 280, 210,  98,  21;
  ...
		

Crossrefs

Cf. A081663, A081659.

Cf. A000045.

Programs

Maple

with(combinat): T:=(n,k)->binomial(n,k)*fibonacci(k+1)+(k+1)*binomial(n,k+1): for n from 0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

Extensions

Edited by N. J. A. Sloane, Nov 29 2006