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

2,2

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 (21,105,-125).

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A095655 A221766 A080483 * A034789 A297635 A292062

Adjacent sequences: A015252 A015253 A015254 * A015256 A015257 A015258

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved