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A006004
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C(n+2,3)+C(n,3)+C(n-1,3).
(Formerly M3412)
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1
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1, 4, 11, 25, 49, 86, 139, 211, 305, 424, 571, 749, 961, 1210, 1499, 1831, 2209, 2636, 3115, 3649, 4241, 4894, 5611, 6395, 7249, 8176, 9179, 10261, 11425, 12674, 14011, 15439, 16961, 18580, 20299, 22121
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OFFSET
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1,2
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COMMENTS
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Equals binomial transform of [1, 3, 4, 3, 0, 0, 0,...]. Example: a(4) = 25 = (1, 3, 3, 1) dot (1, 3, 4, 3) = (1 + 9 + 12 + 3). - Gary W. Adamson, Jul 25 2008
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REFERENCES
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S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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(n^3-2n^2+5n-2)/2.
G.f.: (x^3+x^2+1)/(x-1)^4 [From Harvey P. Dale, June 15 2011]
a(0)=1, a(1)=4, a(2)=11, a(3)=25, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4) [From Harvey P. Dale, June 15 2011]
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MATHEMATICA
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Table[Binomial[n+2, 3]+Binomial[n, 3]+Binomial[n-1, 3], {n, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 11, 25}, 50] (* From Harvey P. Dale, June 15 2011 *)
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CROSSREFS
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Sequence in context: A115294 A110610 A051462 * A006522 A036837 A215052
Adjacent sequences: A006001 A006002 A006003 * A006005 A006006 A006007
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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