A015264 Gaussian binomial coefficient [ n,2 ] for q = -12.

1, 133, 19285, 2775445, 399683221, 57554154133, 8287800951445, 1193443303932565, 171855836163195541, 24747240402737283733, 3563602618051323347605, 513158776998704708174485, 73894863887821708223693461

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 (133, 1596, -1728).

Formula

G.f.: x^2/((1-x)*(1+12*x)*(1-144*x)).

a(2) = 1, a(3) = 133, a(4) = 19285, a(n) = 133*a(n-1) + 1596*a(n-2) - 1728*a(n-3). - Vincenzo Librandi, Oct 28 2012

Mathematica

Table[QBinomial[n, 2, -12], {n, 2, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Prog

(Sage) [gaussian_binomial(n, 2, -12) for n in range(2, 14)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 133, 19285]; [n le 3 select I[n] else 133*Self(n-1)+1596*Self(n-2)-1728*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 28 2012

Crossrefs

Sequence in context: A129050 A129049 A281496 * A055579 A191715 A208626

Adjacent sequences: A015261 A015262 A015263 * A015265 A015266 A015267

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved