A015261 Gaussian binomial coefficient [ n,2 ] for q = -10.

1, 91, 9191, 918191, 91828191, 9182728191, 918273728191, 91827363728191, 9182736463728191, 918273645463728191, 91827364555463728191, 9182736455455463728191, 918273645546455463728191

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 (91,910,-1000).

Formula

G.f.: x^2/((1-x)*(1+10*x)*(1-100*x)).

a(2) = 1, a(3) = 91, a(4) = 9191, a(n) = 91*a(n-1) + 910*a(n-2) - 1000*a(n-3). - Vincenzo Librandi, Oct 28 2012

Mathematica

Table[QBinomial[n, 2, -10], {n, 2, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Prog

(Sage) [gaussian_binomial(n, 2, -10) for n in range(2, 15)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 91, 9191]; [n le 3 select I[n] else 91*Self(n-1) + 910*Self(n-2) - 1000*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 28 2012

Crossrefs

Sequence in context: A109627 A095372 A165154 * A370780 A168624 A131442

Adjacent sequences: A015258 A015259 A015260 * A015262 A015263 A015264

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved