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 (157, 2041, -2197).
FORMULA
G.f.: x^2/((1-x)*(1+13*x)*(1-169*x)). - Ralf Stephan, Apr 01 2004
a(2) = 1, a(3) = 157, a(4) = 26690, a(n) = 157*a(n-1) + 2041*a(n-2) - 2197*a(n-3). - Vincenzo Librandi, Oct 28 2012
a(n) = (1/2352)*( (1 - (-13)^n)*((-13)^(n-1) - 1) ). - M. F. Hasler, Nov 03 2012
MATHEMATICA
Table[QBinomial[n, 2, -13], {n, 2, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
PROG
(Sage) [gaussian_binomial(n, 2, -13) for n in range(2, 14)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 157, 26690]; [n le 3 select I[n] else 157*Self(n-1)+2041*Self(n-2)-2197*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 28 2012
(PARI) A015265(n, q=-13)=(1-q^n)*(q^(n-1)-1)/2352 \\ M. F. Hasler, Nov 03 2012
CROSSREFS
Cf. Gaussian binomial coefficients [n,2] for q=-2,...,-12: A015249, A015251, A015253, A015255, A015257 A015258, A015259, A015260, A015261, A015262, A015264.
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved