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
T. D. Noe, Table of n, a(n) for n = 4..204
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 (31,-310,1240,-1984,1024).
FORMULA
G.f.: x^4/((1-x)*(1-2*x)*(1-4*x)*(1-8*x)*(1-16*x)).
a(n) = (2^n-1)*(2^n-2)*(2^n-4)*(2^n-8)/20160. - Bruno Berselli, Aug 29 2011
MAPLE
A006097:=-1/(z-1)/(4*z-1)/(2*z-1)/(8*z-1)/(16*z-1); # Simon Plouffe in his 1992 dissertation with offset 0
MATHEMATICA
faq[n_, q_] = Product[(1-q^(1+k))/(1-q), {k, 0, n-1}];
qbin[n_, m_, q_] = faq[n, q]/(faq[m, q]*faq[n-m, q]);
Table[qbin[n, 4, 2], {n, 4, 21}] (* Jean-François Alcover, Jul 21 2011 *)
QBinomial[Range[4, 30], 4, 2] (* Harvey P. Dale, Dec 10 2012 *)
PROG
(Sage) [gaussian_binomial(n, 4, 2) for n in range(4, 22)] # Zerinvary Lajos, May 24 2009
(Magma) r:=4; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 06 2016
(PARI) a(n)=(2^n-1)*(2^n-2)*(2^n-4)*(2^n-8)/20160 \\ Charles R Greathouse IV, Feb 19 2017
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved