OFFSET
3,2
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 = 3..1000
Index entries for linear recurrences with constant coefficients, signature (-5, 30, 40, -64).
FORMULA
From Paul Barry, Jul 12 2005: (Start)
G.f.: x^3/((1-2*x-8*x^2)*(1+7*x-8*x^2));
a(n) = -5*a(n-1) + 30*a(n-2) + 40*a(n-3) - 64*a(n-4);
a(n+3) = (-1)^n*J(n)*J(n+1)*J(n+2)/3, where J(n)=A001045(n). (End)
a(n) = T015109(n,3), where T015109 is the triangular array defined by A015109. - M. F. Hasler, Nov 04 2012
MATHEMATICA
Table[QBinomial[n, 2, -2], {n, 3, 25}] (* G. C. Greubel, Jul 31 2016 *)
PROG
(Sage) [gaussian_binomial(n, 3, -2) for n in range(3, 22)] # Zerinvary Lajos, May 27 2009
(Magma) [(1/81)*(24*4^n-6*(-2)^n+64*(-8)^n-1): n in [0..20]]; // Vincenzo Librandi, Aug 23 2011
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved