A094443 Triangular array T(n,k) = Fibonacci(n+3-k)*C(n,k), k=0..n, n>=0.

2, 3, 2, 5, 6, 2, 8, 15, 9, 2, 13, 32, 30, 12, 2, 21, 65, 80, 50, 15, 2, 34, 126, 195, 160, 75, 18, 2, 55, 238, 441, 455, 280, 105, 21, 2, 89, 440, 952, 1176, 910, 448, 140, 24, 2, 144, 801, 1980, 2856, 2646, 1638, 672, 180, 27, 2, 233, 1440, 4005, 6600, 7140, 5292, 2730, 960, 225, 30, 2

Offset

0,1

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

From G. C. Greubel, Oct 30 2019: (Start)

T(n,k) = binomial(n,k)*Fibonacci(n-k+3).

Sum_{k=0..n} T(n,k) = Fibonacci(2*n+3).

Sum_{k=0..n} (-1)^k * T(n,k) = (-1)^n * Fibonacci(n-3). (End)

Example

First few rows:
   2;
   3,  2;
   5,  6,  2;
   8, 15,  9,  2;
  13, 32, 30, 12,  2;
  21, 65, 80, 50, 15, 2;

Maple

with(combinat): seq(seq(fibonacci(n-k+3)*binomial(n, k), k=0..n), n=0..12); # G. C. Greubel, Oct 30 2019

Mathematica

Table[Fibonacci[n-k+3]*Binomial[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 30 2019 *)

Prog

(PARI) T(n, k) = binomial(n, k)*fibonacci(n-k+3);
for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Oct 30 2019
(Magma) [Binomial(n, k)*Fibonacci(n-k+3): k in [0..n], n in [0..12]]; // G. C. Greubel, Oct 30 2019
(Sage) [[binomial(n, k)*fibonacci(n-k+3) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Oct 30 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, k)*Fibonacci(n-k+3) ))); # G. C. Greubel, Oct 30 2019

Crossrefs

Cf. A000045, A094435, A094436, A094437, A094438, A094439, A094440, A094441, A094442, A094444.

Sequence in context: A307864 A066119 A003970 * A348066 A227071 A276270

Adjacent sequences: A094440 A094441 A094442 * A094444 A094445 A094446

Keyword

nonn,tabl

Author

Clark Kimberling, May 03 2004

Status

approved