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

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 (73, 657, -729).

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,2,-9) for n in range(2,15)] # Zerinvary Lajos, May 27 2009

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