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.
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=2..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 (13,-39,27).
FORMULA
G.f.: x^2/[(1-x)(1-3x)(1-9x)].
a(n) = (9^n - 4*3^n + 3)/48. - Mitch Harris, Mar 23 2008
a(n) = 4*a(n-1) -3*a(n-2) +9^(n-2), n>=4. - Vincenzo Librandi, Mar 20 2011
MAPLE
a:=n->sum((9^(n-j)-3^(n-j))/6, j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 15 2007
A006100:=-1/(z-1)/(3*z-1)/(9*z-1); # Simon Plouffe in his 1992 dissertation with offset 0
MATHEMATICA
PROG
(Sage) [gaussian_binomial(n, 2, 3) for n in range(2, 19)] # Zerinvary Lajos, May 25 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved