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

0,2

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).

Links

Table of n, a(n) for n=0..63.

Example

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;
  ...

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

Crossrefs

Cf. A081663, A081659.

Cf. A000045.

Sequence in context: A131394 A130585 A209151 * A128544 A120058 A208532

Adjacent sequences: A125097 A125098 A125099 * A125101 A125102 A125103

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 20 2006

Extensions

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

Status

approved