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.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 3..200
Index entries for linear recurrences with constant coefficients, signature (-2040,346970,4481880,-4826809)
FORMULA
a(n) = Product_{i=1..3} ((-13)^(n-i+1) - 1)/((-13)^i - 1). - M. F. Hasler, Nov 03 2012
G.f.: x^3 / ( (x-1)*(2197*x+1)*(13*x+1)*(169*x-1) ). - R. J. Mathar, Aug 03 2016
EXAMPLE
MATHEMATICA
QBinomial[Range[3, 15], 3, -13] (* Harvey P. Dale, Jun 21 2012 *)
Table[QBinomial[n, 3, -13], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
PROG
(Sage) [gaussian_binomial(n, 3, -13) for n in range(3, 13)] # Zerinvary Lajos, May 27 2009
(PARI) A015286(n, r=3, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
(Magma) r:=3; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016
CROSSREFS
Cf. Gaussian binomial coefficients [n,r] for q=-13: A015265 (r=2), A015303 (r=4), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012
Fourth row (r=3) or column (resp. diagonal) in A015129 (read as square array resp. triangle). - M. F. Hasler, Nov 03 2012
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved