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A048908
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Indices of triangular numbers which are also 9-gonal.
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2
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1, 25, 406, 6478, 103249, 1645513, 26224966, 417953950, 6661038241, 106158657913, 1691877488374, 26963881156078, 429730221008881, 6848719654986025, 109149784258767526, 1739547828485294398
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OFFSET
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1,2
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COMMENTS
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lim( n -> Infinity , a(n)/a(n-1)) = 8 + 3*sqrt(7). - Ant King, Nov 03 2011
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LINKS
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Table of n, a(n) for n=1..16.
Eric Weisstein's World of Mathematics, Nonagonal Triangular Number.
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FORMULA
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a(n+2)=16*a(n+1)-a(n)+7, a(n+1)=8*a(n)+3.5+1.5*(28*a(n)^2+28*a(n)+25)^0.5 - Richard Choulet, Sep 22 2007
G.f.: f(z)=a(1)*z+a(2)*z^2+...= (z+8z^2-2*z^3)/((1-z)*(1-16*z+z^2)) - Richard Choulet, Oct 09 2007
a(n)=-(1/2)+(3/4)*{[8-3*sqrt(7)]^n+[8+3*sqrt(7)]^n}+(9/28)*sqrt(7)*{[8+3*sqrt(7)]^n- [8-3*sqrt(7)]^n}, with n>=0 [From Paolo P. Lava, Nov 25 2008]
From Ant King, Nov 03 2011: (Start)
a(n) = 17*a(n-1) - 17*a(n-2) + a(n-3)
a(n)=floor(3/28*sqrt(7)*(3 - sqrt(7))*(8 + 3* sqrt(7))^n)
(End)
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MATHEMATICA
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LinearRecurrence[{17, -17, 1}, {1, 25, 406}, 16]; (* Ant King, Nov 03 2011 *)
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CROSSREFS
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Cf. A048907, A048909.
Sequence in context: A028064 A028061 A026561 * A026391 A028044 A028057
Adjacent sequences: A048905 A048906 A048907 * A048909 A048910 A048911
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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