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

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

Offset

2,2

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 (111, 1221, -1331).

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A172175 A178906 A225374 * A201430 A262641 A145698

Adjacent sequences: A015259 A015260 A015261 * A015263 A015264 A015265

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved