A015255 Gaussian binomial coefficient [ n,2 ] for q = -5.

1, 21, 546, 13546, 339171, 8476671, 211929796, 5298179796, 132454820421, 3311368882921, 82784230211046, 2069605714586046, 51740143068101671, 1293503575685289171, 32337589397218492296, 808439734905030992296

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 (21,105,-125).

Programs

Magma

I:=[1, 21, 546]; [n le 3 select I[n] else 21*Self(n-1) + 105*Self(n-2) - 125*Self(n-3): n in [1..30]] // Vincenzo Librandi, Oct 27 2012

Mathematica

Table[QBinomial[n,2,-5],{n,2,22}] (* or *) LinearRecurrence[ {21,105,-125}, {1,21,546},21] (* Harvey P. Dale, Jun 24 2011 *)

Sage

[gaussian_binomial(n,2,-5) for n in range(2,18)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^2/((1-x)*(1+5*x)*(1-25*x)).

a(0)=1, a(1)=21, a(2)=546, a(n) = 21*a(n-1) + 105*a(n-2) - 125*a(n-3). - Harvey P. Dale, Jun 24 2011