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A006096
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Gaussian binomial coefficient [ n,3 ] for q=2.
(Formerly M4982)
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3
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1, 15, 155, 1395, 11811, 97155, 788035, 6347715, 50955971, 408345795, 3269560515, 26167664835, 209386049731, 1675267338435, 13402854502595, 107225699266755, 857817047249091, 6862582190715075, 54900840777134275, 439207459223777475
(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..203
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.
Index to sequences with linear recurrences with constant coefficients, signature (15,-70,120,-64).
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FORMULA
| G.f.: x^3/((1-x)(1-2x)(1-4x)(1-8x)).
(With a different offset) a(n)=(-1+7*2^n-14*4^n+8*8^n)/21 - Jim Buddenhagen, Dec 14 2003
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MAPLE
| seq((-1+7*2^n-14*4^n+8*8^n)/21, n=1..20);
A006096:=1/(z-1)/(8*z-1)/(2*z-1)/(4*z-1); [S. Plouffe in his 1992 dissertation with offset 0.]
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MATHEMATICA
| Drop[CoefficientList[Series[x^3/((1 - x) (1 - 2 x) (1 - 4 x) (1 - 8 x)), {x, 0, 30}], x], 3]
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PROG
| (Sage) [gaussian_binomial(n, 3, 2) for n in xrange(3, 23)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 24 2009]
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CROSSREFS
| Sequence in context: A017389 A157380 A098685 * A099915 A110557 A016304
Adjacent sequences: A006093 A006094 A006095 * A006097 A006098 A006099
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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