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A048914
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Indices of pentagonal numbers which are also 9-gonal.
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2
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1, 21, 10981, 252081, 132846121, 3049673901, 1607172358861, 36894954600201, 19443571064652241, 446355157703555781, 235228321132990450741, 5400004661002663236321, 2845792209623347408410361
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Contribution from Ant King, Dec 20 2011: (Start)
lim(n->Infinity, a(2n+1)/a(2n))=1/2*(527+115*sqrt(21))
lim(n->Infinity, a(2n)/a(2n-1))=1/2*(23+5*sqrt(21))
(End)
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| Contribution from Ant King, Dec 20 2011: (Start)
a(n) = 12098*a(n-2)-a(n-4)-2016
a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5)
a(n) = 1/84*((2+sqrt(21))*(7-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2)+ (2-sqrt(21))*(7+sqrt(21)*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(2n-2)+14)
a(n) = ceiling(1/84*(2+sqrt(21))*(7-sqrt(21)*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2))
GF: x*(1+20*x-1138*x^2-860*x^3-39*x^4) / ((1-x)*(1-110*x+x^2)*(1+110*x+x^2))
(End)
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MATHEMATICA
| LinearRecurrence[{1, 12098, -12098, -1, 1}, {1, 21, 10981, 252081, 132846121}, 13] (* Ant King, Dec 20 2011 *)
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CROSSREFS
| Cf. A048913, A048915.
Sequence in context: A135823 A013726 A159358 * A046183 A203674 A180769
Adjacent sequences: A048911 A048912 A048913 * A048915 A048916 A048917
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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