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A046189
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Octagonal pentagonal numbers.
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3
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1, 176, 1575425, 234631320, 2098015778145, 312461813932000, 2793956983975264801, 416109772078405066376, 3720751630955537773670465, 554139209013308662750166160, 4954977037463529073741814611905
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OFFSET
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1,2
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COMMENTS
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From Ant King, Dec 16 2011: (Start)
lim(n->Infinity, a(2n+1)/a(2n))=1/49*(219073+154908*sqrt(2))
lim(n->Infinity, a(2n)/a(2n-1))=1/49*(3649+2580*sqrt(2))
(End)
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LINKS
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Table of n, a(n) for n=1..11.
Eric Weisstein's World of Mathematics, Octagonal Pentagonal Number.
Index to sequences with linear recurrences with constant coefficients, signature (1,1331714,-1331714,-1,1).
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FORMULA
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Contribution from Ant King, Dec 16 2011: (Start)
a(n) = 1331714*a(n-2) - a(n-4) + 249696.
a(n) = a(n-1) + 1331714*a(n-2) - 1331714*a(n-3) - a(n-4) + a(n-5).
a(n) = 1/96*((11-6*sqrt(2)*(-1)^n)*(1+sqrt(2))^(8*n-6)+(11+6*sqrt(2)*(-1)^n)*(1-sqrt(2))^(8*n-6)-18).
a(n) = floor(1/96*(11-6*sqrt(2)*(-1)^n)*(1+sqrt(2))^(8*n-6)).
GF: x*(1+175*x+243535*x^2+5945*x^3+40*x^4)/((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)).
(End)
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MATHEMATICA
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LinearRecurrence[{1, 1331714, -1331714, -1, 1}, {1, 176, 1575425, 234631320, 2098015778145}, 11] (* Ant King, Dec 16 2011 *)
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CROSSREFS
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Cf. A046187, A046188.
Sequence in context: A159426 A009722 A159442 * A164843 A077786 A188537
Adjacent sequences: A046186 A046187 A046188 * A046190 A046191 A046192
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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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