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A048913
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Indices of 9-gonal numbers which are also pentagonal.
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2
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1, 14, 7189, 165026, 86968201, 1996480214, 1052141284189, 24153417459626, 12728805169146001, 292208042430070814, 153993083884187031589, 3535132873165579243826, 1863008316102089539013401
(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)-4320
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))*(sqrt(21)-3*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2)-(2-sqrt(21))*( sqrt(21)+3*(-1)^n)*(2*sqrt(7)-3*sqrt(3))^(2n-2)+30)
a(n) = ceiling(1/84*(2+sqrt(21))*(sqrt(21)-3*(-1)^n)*(2*sqrt(7)+3*sqrt(3))^(2n-2))
GF: x*(1+13*x-4923*x^2+563*x^3+26*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, 14, 7189, 165026, 86968201}, 13] (* Ant King, Dec 20 2011 *)
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CROSSREFS
| Cf. A048914, A048915.
Sequence in context: A030531 A206357 A147686 * A104376 A053870 A079176
Adjacent sequences: A048910 A048911 A048912 * A048914 A048915 A048916
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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