A022243 Gaussian binomial coefficients [ n,3 ] for q = 8.

1, 585, 304265, 156087945, 79936505481, 40928737412745, 20955593338439305, 10729268895402608265, 5493386001237942388361, 2812613653548502301460105, 1440058191955372430686340745, 737309794366817196670904616585, 377502614721293061473789582165641, 193281338737652937508391225143510665

Offset

3,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..200

Index entries for linear recurrences with constant coefficients, signature (585,-37960,299520,-262144).

Formula

a(n) = Product_{i=1..3} (8^(n-i+1)-1)/(8^i-1), by definition. - Vincenzo Librandi, Aug 05 2016

Mathematica

Table[QBinomial[n, 3, 8], {n, 3, 20}] (* Vincenzo Librandi, Aug 05 2016 *)

Prog

(SageMath) [gaussian_binomial(n, 3, 8) for n in range(3, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 05 2016

Crossrefs

Sequence in context: A258331 A352979 A379950 * A217446 A369861 A171436

Adjacent sequences: A022240 A022241 A022242 * A022244 A022245 A022246

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 05 2016

Status

approved