A006102 Gaussian binomial coefficient [ n,4 ] for q=3. (Formerly M5384)

1, 121, 11011, 925771, 75913222, 6174066262, 500777836042, 40581331447162, 3287582741506063, 266307564861468823, 21571273555248777493, 1747282899667791058573, 141530177899268957392924, 11463951511551877750726204, 928580264181940191843785764, 75215006575885931519565302404

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..100

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)

Maple

A006102:=-1/((z-1)*(81*z-1)*(3*z-1)*(9*z-1)*(27*z-1)); # conjectured (correctly) by Simon Plouffe in his 1992 dissertation

Mathematica

Table[QBinomial[n, 4, 3], {n, 4, 24}] (* Vincenzo Librandi, Aug 02 2016 *)

Prog

(Sage) [gaussian_binomial(n, 4, 3) for n in range(4, 20)] # Zerinvary Lajos, May 25 2009
(Magma) r:=4; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

Crossrefs

Partial sums of A226804. - Christian Krause, Dec 26 2022

Sequence in context: A176923 A058412 A231661 * A263819 A036508 A054319

Adjacent sequences: A006099 A006100 A006101 * A006103 A006104 A006105

Keyword

nonn

Author

N. J. A. Sloane

Status

approved