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A046183
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Octagonal triangular numbers.
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2
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1, 21, 11781, 203841, 113123361, 1957283461, 1086210502741, 18793835590881, 10429793134197921, 180458407386358101, 100146872588357936901, 1732761608929974897121, 961610260163619775927681
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| From Ant King, Oct 31 2011: (Start)
limit n -> infinity, u(2n+1)/u(2n)) = 1/25*(6937+2832*sqrt(6)).
limit n -> infinity, u(2n)/u(2n-1)) = 1/25*(217+88*sqrt(6)).
(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
| a(n+1)=4801*a(n)+1100+980*(24*a(n)^2+11*a(n)+1)^0.5. G.f.: f(z)=a(1)*z+a(2)*z^2+...= (z+21*z^2+2178*z^3+2178*z^4+21*z^5+z^6)/((1-z^2)*(1-9602*z^2+z^4)) (the numerator is divible by 1+z but it is more symetri" like that) - Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 03 2007
From Ant King, Oct 31 2011: (Start)
a(n) = a(n-1) + 9602a(n-2) - 9602a(n-3) - a(n-4) + a(n-5).
a(n) = 9602*a(n-2) - a(n-4) + 2200.
a(n) = 1/96*((7-2*sqrt(6)*(-1)^n)*(sqrt(3)+sqrt(2))^(4*n-2)+(7+2*sqrt(6)*(-1)^n)*(sqrt(3)-sqrt(2))^(4*n-2)-22).
a(n) = floor(1/96*(7-2*sqrt(6)*(-1)^n)*(sqrt(3)+sqrt(2))^(4n-2))
(End)
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MATHEMATICA
| LinearRecurrence[{1, 9602, -9602, -1, 1}, {1, 21, 11781, 203841, 113123361}, 13] (* Ant King, Oct 31 2011 *)
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CROSSREFS
| Cf. A046181, A046182.
Sequence in context: A013726 A159358 A048914 * A203674 A180769 A185557
Adjacent sequences: A046180 A046181 A046182 * A046184 A046185 A046186
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| More terms from Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 03 2007
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