OFFSET
4,2
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 = 4..200
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
FORMULA
G.f.: x^4/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)). - Vincenzo Librandi, Aug 07 2016
a(n) = Product_{i=1..4} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 06 2016
MAPLE
qBinom := proc(n, m, q)
mul( (1-q^(n-i))/(1-q^(i+1)), i=0..m-1) ;
end proc:
A006113 := proc(n)
qBinom(n, 4, 5) ;
end proc:
seq(A006113(n), n=4..16) ; # R. J. Mathar, Sep 28 2011
MATHEMATICA
Table[QBinomial[n, 4, 5], {n, 4, 20}] (* Vincenzo Librandi, Aug 07 2016 *)
PROG
(Sage) [gaussian_binomial(n, 4, 5) for n in range(4, 14)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; 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