A015259 Gaussian binomial coefficient [ n,2 ] for q = -8.

1, 57, 3705, 236665, 15150201, 969583737, 62053592185, 3971428035705, 254171409198201, 16266970069380217, 1041086085394771065, 66629509457629850745, 4264288605349394427001, 272914470741872571493497

Offset

2,2

References

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..200

Index entries for linear recurrences with constant coefficients, signature (57,456,-512).

Formula

G.f.: x^2/((1-x)*(1+8*x)*(1-64*x)).

a(2) = 1, a(3) = 57, a(4) = 3705, a(n) = 57*a(n-1) + 456*a(n-2) - 512*a(n-3). - Vincenzo Librandi, Oct 27 2012

Mathematica

Table[QBinomial[n, 2, -8], {n, 2, 20}] (* Vincenzo Librandi, Oct 27 2012 *)

Prog

(Sage) [gaussian_binomial(n, 2, -8) for n in range(2, 16)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 57, 3705]; [n le 3 select I[n] else 57*Self(n-1)+456*Self(n-2)-512*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 27 2012

Crossrefs

Sequence in context: A239823 A012058 A122533 * A218808 A218194 A218370

Adjacent sequences: A015256 A015257 A015258 * A015260 A015261 A015262

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved