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
Vincenzo Librandi, Table of n, a(n) for n = 2..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 (21,-84,64)
FORMULA
G.f.: x^2/((1-x)*(1-4*x)*(1-16*x)). [Multiplied by x^2 to match offset by R. J. Mathar, Mar 11 2009]
a(n) = (16^n - 5*4^n + 4)/180. - Mitch Harris, Mar 23 2008
a(n) = 5*a(n-1) -4*a(n-2) +16^(n-2), n>=4. - Vincenzo Librandi, Mar 20 2011
MAPLE
A006105:=-1/(z-1)/(4*z-1)/(16*z-1); # Simon Plouffe in his 1992 dissertation, assuming offset zero
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, 2, 4], {n, 2, 16}] (* Jean-François Alcover, Jul 21 2011 *)
CoefficientList[Series[1 / ((1 - x) (1 - 4 x) (1 - 16 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 23 2013 *)
LinearRecurrence[{21, -84, 64}, {1, 21, 357}, 20] (* Harvey P. Dale, Feb 17 2020 *)
PROG
(Sage) [gaussian_binomial(n, 2, 4) for n in range(2, 17)] # Zerinvary Lajos, May 28 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved