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A005714
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Coefficient of x^6 in expansion of (1+x+x^2)^n.
(Formerly M4704)
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8
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1, 10, 45, 141, 357, 784, 1554, 2850, 4917, 8074, 12727, 19383, 28665, 41328, 58276, 80580, 109497, 146490, 193249, 251713, 324093, 412896, 520950, 651430, 807885, 994266, 1214955, 1474795, 1779121, 2133792, 2545224, 3020424, 3567025
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| a(n) = A111808(n,6) for n>5. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 17 2005
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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.
Eric Weisstein's World of Mathematics, Trinomial Coefficient
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FORMULA
| a(n)= binomial(n, 3)*(n^3+18*n^2+17*n-120) /120.
G.f.: (x^3)*(1+3*x-4*x^2+x^3)/(1-x)^7 (Numerator polynomial is N3(6, x) from A063420.)
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MAPLE
| A005714:=-(1+3*z-4*z**2+z**3)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| a[n_] := Coefficient[(1 + x + x^2)^n, x, 6]; Table[a[n], {n, 3, 35}]
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CROSSREFS
| Cf. A000574, A005581, A005712, A005715-A005716.
a(n)= A027907(n, 6), n >= 3 (seventh column of trinomial coefficients).
Sequence in context: A179095 A037270 A027800 * A175705 A143671 A141499
Adjacent sequences: A005711 A005712 A005713 * A005715 A005716 A005717
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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
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 02 2000
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