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A046193
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Indices of heptagonal numbers (A000566) which are also triangular.
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2
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1, 5, 221, 1513, 71065, 487085, 22882613, 156839761, 7368130225, 50501915861, 2372515049741, 16261460067385, 763942477886281, 5236139639782013, 245987105364332645, 1686020702549740705, 79207083984837225313
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| From Ant King, Oct 19 2011: (Start)
lim(n->Infinity,a(2n+1)/a(2n))=1/2(47+21*sqrt(5))
lim(n->Infinity,a(2n)/a(2n-1))=1/2(7+3*sqrt(5))
(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
| For n odd, a(n+2)=322*a(n+1)-a(n)-96; for n even, a(n+1)=161*a(n)-48+36*(20*a(n)^2-12*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 29 2007, Oct 09 2007
From Ant King, Oct 19 2011: (Start)
a(n)=322a(n-2)-a(n-4)-96
a(n)=a(n-1)+322a(n-2)-322a(n-3)-a(n-4)+a(n-5)
a(n)=1/20*((sqrt(5)-(-1)^n)*(sqrt(5)+2)^(2n-1)+ (sqrt(5)+(-1)^n)*(sqrt(5)-2)^(2n-1)+6)
a(n)=ceiling(1/20*(sqrt(5)-(-1)^n)*(2+sqrt(5))^(2n-1))
GF:x*(1+4*x-106*x^2+4*x^3+x^4)/((1-x)*(1-18*x+x^2)*(1+18*x+x^2))
(End)
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MATHEMATICA
| LinearRecurrence[{1, 322, -322, -1, 1}, {1, 5, 221, 1513, 71065}, 17] (* Ant King, Oct 19 2011 *)
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CROSSREFS
| Cf. A039835, A046194.
Sequence in context: A024070 A050617 A066462 * A195633 A112999 A185551
Adjacent sequences: A046190 A046191 A046192 * A046194 A046195 A046196
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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