A015253 Gaussian binomial coefficient [ n,2 ] for q = -4.

1, 13, 221, 3485, 55965, 894621, 14317213, 229062301, 3665049245, 58640578205, 938250090141, 15011998086813, 240191982810781, 3843071671285405, 61489146955314845, 983826350426044061, 15741221610252678813

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 (13,52,-64).

Formula

G.f.: x^2/((1-x)*(1+4*x)*(1-16*x)).

a(2) = 1, a(3) = 13, a(4) = 221 a(n) = 13*(n-1) + 52*a(n-2) - 64*a(n-3). - Vincenzo Librandi, Oct 27 2012

Example

G.f. = x^2 + 13*x^3 + 221*x^4 + 3485*x^5 + 55965*x^6 + 894621*x^7 + ...

Mathematica

Rest[Table[QBinomial[n, 2, -4], {n, 20}]] (* Harvey P. Dale, Feb 26 2012 *)

Prog

(Sage) [gaussian_binomial(n, 2, -4) for n in range(2, 19)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 13, 221]; [n le 3 select I[n] else 13*Self(n-1) + 52*Self(n-2) - 64*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Oct 27 2012

Crossrefs

Sequence in context: A059525 A086147 A329073 * A051621 A173427 A051180

Adjacent sequences: A015250 A015251 A015252 * A015254 A015255 A015256

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved