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A006101
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Gaussian binomial coefficient [ n,3 ] for q=3.
(Formerly M5272)
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1
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1, 40, 1210, 33880, 925771, 25095280, 678468820, 18326727760, 494894285941, 13362799477720, 360801469802830, 9741692640081640, 263026177881648511, 7101711092201899360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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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.
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LINKS
| T. D. Noe, Table of n, a(n) for n=3..100
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| G.f.: z^3/((1-z)(1-3z)(1-9z)(1-27z)); a(n) = (27^n - 13*9^n + 39*3^n - 27)/11232 - Mitch Harris (maharri(AT)gmail.com), Mar 23 2008
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MAPLE
| A006101:=1/(z-1)/(3*z-1)/(27*z-1)/(9*z-1); [S. Plouffe in his 1992 dissertation, assuming offset zero.]
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PROG
| (Other) sage: [gaussian_binomial(n, 3, 3) for n in xrange(3, 17)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2009]
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CROSSREFS
| Sequence in context: A004385 A152257 A061650 * A188253 A049396 A135644
Adjacent sequences: A006098 A006099 A006100 * A006102 A006103 A006104
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Removed attribute "conjectured" from Plouffe G.f R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 11 2009
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