A015260 Gaussian binomial coefficient [ n,2 ] for q = -9.

1, 73, 5986, 484210, 39226915, 3177326971, 257363962948, 20846476694116, 1688564650965445, 136773736379522605, 11078672649879436966, 897372484611991440598, 72687171253825493271271, 5887660871557577275727455, 476900530596184348447133320

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 (73, 657, -729).

Formula

G.f.: x^2/((1-x)*(1+9*x)*(1-81*x)).

a(2) = 1, a(3) = 73, a(4) = 5986, a(n) = 73*a(n-1) + 657*a(n-2) - 729*a(n-3). - Vincenzo Librandi, Oct 27 2012

Mathematica

Table[QBinomial[n, 2, -9], {n, 2, 20}] (* Vincenzo Librandi, Oct 27 2012 *)

Prog

(Sage) [gaussian_binomial(n, 2, -9) for n in range(2, 15)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 73, 5986]; [n le 3 select I[n] else 73*Self(n-1) + 657*Self(n-2) - 729*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 27 2012

Crossrefs

Sequence in context: A093273 A183540 A022242 * A089788 A292013 A192765

Adjacent sequences: A015257 A015258 A015259 * A015261 A015262 A015263

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved