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A006101 Gaussian binomial coefficient [ n,3 ] for q=3.
(Formerly M5272)
2
1, 40, 1210, 33880, 925771, 25095280, 678468820, 18326727760, 494894285941, 13362799477720, 360801469802830, 9741692640081640, 263026177881648511, 7101711092201899360, 191746238094034963240, 5177148775980218655520, 139783020078437440101481 (list; graph; refs; listen; history; text; internal format)
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
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)
FORMULA
G.f.: z^3/((1-z)(1-3z)(1-9z)(1-27z)). Simon Plouffe in his 1992 dissertation
a(n) = (27^n - 13*9^n + 39*3^n - 27)/11232. - Mitch Harris, Mar 23 2008
MATHEMATICA
Table[QBinomial[n, 3, 3], {n, 3, 20}] (* Vincenzo Librandi, Nov 06 2016 *)
PROG
(Sage) [gaussian_binomial(n, 3, 3) for n in range(3, 17)] # Zerinvary Lajos, May 25 2009
(Magma) r:=3; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2016
CROSSREFS
Sequence in context: A229457 A331350 A061650 * A278381 A251202 A239189
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 15 20:38 EDT 2024. Contains 371696 sequences. (Running on oeis4.)