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A046182
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Indices of triangular numbers which are also octagonal.
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3
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1, 6, 153, 638, 15041, 62566, 1473913, 6130878, 144428481, 600763526, 14152517273, 58868694718, 1386802264321, 5768531318886, 135892469386233, 565257200556158, 13316075197586561, 55389437123184646
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| From Ant King, Nov 01 2011: (Start)
lim(n->Infinity,a(2n+1)/a(2n))=1/5*(59+24*sqrt(6))
lim(n->Infinity,a(2n)/a(2n-1))=1/5*(11+4*sqrt(6))
(End)
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Octagonal Triangular Number
Index to sequences with linear recurrences with constant coefficients, signature (1,98,-98,-1,1).
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FORMULA
| For n odd, a(n+2)=98*a(n+1)-a(n)+48; for n even, a(n+1)=49*a(n)+24+10*(24*a(n)^2+24*a(n)+16)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 03 2007, Oct 09 2007
From Ant King, Nov 01 2011: (Start)
a(n) = a(n-1) + 98*a(n-2) - 98*a(n-3) - a(n-4) + a(n-5)
a(n) = 98*a(n-2) - a(n-4) + 48
a(n) = 1/12*sqrt(3)(( sqrt(6)-(-1)^n)*(sqrt(3)+sqrt(2))^(2*n-1)-(sqrt(6)+(-1)^n)*(sqrt(3)-sqrt(2))^(2*n-1)-2*sqrt(3))
a(n)=floor(1/12* sqrt(3)*(sqrt(6)-(-1)^n)*(sqrt(3)+sqrt(2))^(2*n-1))
GF:x(1+5*x+49*x^2-5*x^3-2*x^4)/((1-x)(1-10*x+x^2)(1+10*x+x^2))
(End)
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MATHEMATICA
| LinearRecurrence[{1, 98, -98, -1, 1}, {1, 6, 153, 638, 15041}, 18](* Ant King, Nov 01 2011 *)
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PROG
| (PARI) Vec((1+5*x+49*x^2-5*x^3-2*x^4)/((1-x)*(1-10*x+x^2)*(1+10*x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Nov 01 2011
(MAGMA) I:=[1, 6, 153, 638, 15041]; [n le 5 select I[n] else Self(n-1)+98*Self(n-2)-98*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // Vincenzo Librandi, Dec 30 2011
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CROSSREFS
| Cf. A046181, A046183, A046190.
Sequence in context: A168654 A147796 A003766 * A092122 A003460 A157626
Adjacent sequences: A046179 A046180 A046181 * A046183 A046184 A046185
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KEYWORD
| nonn,easy
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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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