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A046187
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Indices of pentagonal numbers which are also octagonal.
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2
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1, 11, 1025, 12507, 1182657, 14432875, 1364784961, 16655525051, 1574960662145, 19220461475787, 1817503239330177, 22180395887532955, 2097397163226361921, 25596157633751554091, 2420394508859982326465
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| From Ant King, Dec 16 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, Link to a section of The World of Mathematics.
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 16 2011: (Start)
a(n) = 1154*a(n-2) - a(n-4) - 192.
a(n) = a(n-1) + 1154*a(n-2) - 1154*a(n-3) - a(n-4) + a(n-5).
a(n) = 1/12*((3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3)+(3+sqrt(2)*(-1)^n)*(1-sqrt(2))^(4*n-3)+2).
a(n) = ceiling(1/12*(3-sqrt(2)*(-1)^n)*(1+sqrt(2))^(4*n-3)).
G.f.: x*(1-8*x-x^2)*(1+18*x+5x^2)/((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, 11, 1025, 12507, 1182657}, 15] (* Ant King, Dec 16 2011 *)
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CROSSREFS
| Cf. A046188, A046189.
Sequence in context: A099440 A069710 A073903 * A004811 A126197 A090814
Adjacent sequences: A046184 A046185 A046186 * A046188 A046189 A046190
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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