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
Vincenzo Librandi, Table of n, a(n) for n = 3..200
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 (156, -4030, 19500, -15625).
FORMULA
G.f.: x^3/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)). - Vincenzo Librandi, Aug 07 2016
a(n) = Product_{i=1..3} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 07 2016
a(n) = (5^n-1)*(5^n-5)*(5^n-25)/1488000. - Robert Israel, Feb 01 2018
MAPLE
A006112:=1/(z-1)/(125*z-1)/(25*z-1)/(5*z-1); # [conjectured by Simon Plouffe in his 1992 dissertation]
seq((5^n-1)*(5^n-5)*(5^n-25)/1488000, n=3..30); # Robert Israel, Feb 01 2018
MATHEMATICA
Table[QBinomial[n, 3, 5], {n, 3, 20}] (* Vincenzo Librandi, Aug 07 2016 *)
PROG
(Sage) [gaussian_binomial(n, 3, 5) for n in range(3, 14)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 07 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved