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Search: id:A005714
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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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+0
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; listen)
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OFFSET
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3,2
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COMMENT
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a(n) = A111808(n,6) for n>5. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 17 2005
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
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LINKS
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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
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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
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A005714:=-(1+3*z-4*z**2+z**3)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A000574, A005581, A005712, A005715-A005716.
a(n)= A027907(n, 6), n >= 3 (seventh column of trinomial coefficients).
Sequence in context: A022605 A037270 A027800 this_sequence A143671 A141499 A061772
Adjacent sequences: A005711 A005712 A005713 this_sequence A005715 A005716 A005717
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 02 2000
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