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

Author

Olivier Gérard, Dec 11 1999

Keywords

• nonn
• easy

Examples

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

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).

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,2,-4) for n in range(2,19)] # Zerinvary Lajos, May 27 2009

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