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..200
Index entries for linear recurrences with constant coefficients, signature (-455,29640,232960,-262144).
FORMULA
G.f.: x^3/((1-x)*(1+8*x)*(1-64*x)*(1+512*x)). - Bruno Berselli, Oct 30 2012
a(n) = (-1 + 57*8^(2n-3) + (-1)^n*8^(n-2)*(57-8^(2n-1)))/290871. - Bruno Berselli, Oct 30 2012
a(n) = Product_{i=1..3} ((-8)^(n-i+1)-1)/((-8)^i-1) (by definition). - Vincenzo Librandi, Aug 02 2016
MATHEMATICA
Table[QBinomial[n, 3, -8], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
PROG
(Sage) [gaussian_binomial(n, 3, -8) for n in range(3, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=-8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved