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A048915
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9-gonal pentagonal numbers.
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2
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OFFSET
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1,2
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COMMENTS
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Contribution from Ant King, Dec 20 2011: (Start)
lim(n->Infinity, a(2n+1)/a(2n))=1/2*(277727+60605*sqrt(21)).
lim(n->Infinity, a(2n)/a(2n-1))=1/2*(527+115*sqrt(21)).
(End)
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LINKS
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Table of n, a(n) for n=1..9.
Eric Weisstein's World of Mathematics, Nonagonal Pentagonal Number.
Index entries for sequences related to linear recurrences with constant coefficients, signature (1,146361602,-146361602,-1,1).
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FORMULA
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Contribution from Ant King, Dec 20 2011: (Start)
a(n) = 146361602*a(n-2)-a(n-4)+35719200.
a(n) = a(n-1)+146361602*a(n-2)-146361602*a(n-3)-a(n-4)+a(n-5).
a(n) = 1/336*((25+4*sqrt(21))*(5-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(4n-4)+ (25-4*sqrt(21))*(5+sqrt(21)*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(4n-4)-82).
a(n) = floor(1/336*(25+4*sqrt(21))*(5-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(4n-4)).
G.f.: x*(1+650*x+34505798*x^2+1210450*x^3+2301*x^4) / ((1-x)*(1-12098*x+x^2)*(1+12098*x+x^2)).
(End)
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MATHEMATICA
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LinearRecurrence[{1, 146361602, -146361602, -1, 1}, {1, 651, 180868051, 95317119801, 26472137730696901}, 9] (* Ant King, Dec 20 2011 *)
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CROSSREFS
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Cf. A048913, A048914.
Sequence in context: A151736 A010087 A110850 * A002232 A127029 A127030
Adjacent sequences: A048912 A048913 A048914 * A048916 A048917 A048918
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KEYWORD
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nonn,easy
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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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