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

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

Offset: 2

Author

Olivier Gérard, Dec 11 1999

Keywords

• nonn
• easy

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).

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,2,-12) for n in range(2,14)] # Zerinvary Lajos, May 27 2009

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