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A046188
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Indices of octagonal numbers which are also pentagonal.
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2
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1, 8, 725, 8844, 836265, 10205584, 965048701, 11777234708, 1113665364305, 13590918647064, 1285168865358885, 15683908341476764, 1483083756958788601, 18099216635145538208, 1711477370361576686285
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| From Ant King, Dec 17 2011: (Start)
lim(n->Infinity, a(2n+1)/a(2n))=1/7*(331+234*sqrt(2))
lim(n->Infinity, a(2n)/a(2n-1))=1/7*(43+30*sqrt(2))
(End)
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LINKS
| Eric Weisstein's World of Mathematics, Octagonal Pentagonal Number.
Index to sequences with linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).
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FORMULA
| Contribution from Ant King, Dec 17 2011: (Start)
a(n) = 1154*a(n-2) - a(n-4) - 384.
a(n) = a(n-1) + 1154*a(n-2) - 1154*a(n-3) - a(n-4) + a(n-5).
a(n) = 1/24*sqrt(2)*((3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3)-(3+sqrt(2)*(-1)^n)*(1-sqrt(2))^(4*n-3)+4*sqrt(2)).
a(n) = ceiling(1/24*sqrt(2)*((3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3))).
G.f.: x*(1+7*x-437*x^2+41*x^3+4*x^4)/((1-x)*(1-34*x+x^2)*(1+34*x+x^2)).
(End)
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MATHEMATICA
| LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 8, 725, 8844, 836265}, 15] (* Ant King, Dec 17 2011 *)
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CROSSREFS
| Cf. A046187, A046189.
Sequence in context: A037076 A116245 A071308 * A014387 A017007 A023813
Adjacent sequences: A046185 A046186 A046187 * A046189 A046190 A046191
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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