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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
LINKS
T. D. Noe, Table of n, a(n) for n=3..100
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
Index entries for linear recurrences with constant coefficients, signature (40, -390, 1080, -729).
FORMULA
G.f.: z^3/((1-z)(1-3z)(1-9z)(1-27z)). Simon Plouffe in his 1992 dissertation
a(n) = (27^n - 13*9^n + 39*3^n - 27)/11232. - Mitch Harris, Mar 23 2008
MATHEMATICA
Table[QBinomial[n, 3, 3], {n, 3, 20}] (* Vincenzo Librandi, Nov 06 2016 *)
PROG
(Sage) [gaussian_binomial(n, 3, 3) for n in range(3, 17)] # Zerinvary Lajos, May 25 2009
(Magma) r:=3; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved