A015262 Gaussian binomial coefficient [ n,2 ] for q = -11.

1, 111, 13542, 1637362, 198134223, 23974093353, 2900866919644, 351004879413684, 42471590605551405, 5139062461110267955, 621826557818118395106, 75241013495730790109766, 9104162632986302495960347, 1101603678591310956191736717

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 (111, 1221, -1331).

Programs

Magma

I:=[1, 111, 13542]; [n le 3 select I[n] else 111*Self(n-1) + 1221*Self(n-2) - 1331*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 28 2012

Mathematica

Table[QBinomial[n, 2, -11], {n, 2, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,2,-11) for n in range(2,14)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^2/((1-x)*(1+11*x)*(1-121*x)).

a(2) = 1, a(3) = 111, a(4) = 13542, a(n) = 111*a(n-1) + 1221*a(n-2) - 1331*a(n-3). - Vincenzo Librandi, Oct 28 2012