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

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

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 (91,910,-1000).

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,2,-10) for n in range(2,15)] # Zerinvary Lajos, May 27 2009

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