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A039835
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Indices of triangular numbers which are also heptagonal.
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2
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1, 10, 493, 3382, 158905, 1089154, 51167077, 350704366, 16475640049, 112925716858, 5305104928861, 36361730124070, 1708227311453353, 11708364174233842, 550043889183050965, 3770056902373173214
(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, Heptagonal Triangular Number
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FORMULA
| G.f.: (-2x^4-9x^3+161x^2+9x+1)/[(1-x)(1-18x+x^2)(1+18x+x^2)].
a(n+2)=322*a(n+1)-a(n)+160 a(n+1)=161*a(n)+80+36*(20*a(n)^2+20*a(n)+9)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 29 2007
From Ant King, Oct 19 2011: (Start)
a(n)=a(n-1)+322a(n-2)-322a(n-3)-a(n-4)+a(n-5)
a(n)=1/20*sqrt(5)*(( sqrt(5)-(-1)^n)*(2+ sqrt(5))^(2n-1)+( sqrt(5)+(-1)^n)*(2- sqrt(5))^(2n-1)-2* sqrt(5))
a(n)=floor(1/20* sqrt(5)*(sqrt(5)-(-1)^n)*(2+ sqrt(5))^(2n-1))(End)
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MATHEMATICA
| LinearRecurrence[{1, 322, -322, -1, 1}, {1, 10, 493, 3382, 158905}, 16] (* Ant King, Oct 19 2011 *)
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PROG
| (PARI) Vec((-2*x^4-9*x^3+161*x^2+9*x+1)/((1-x)*(1-18*x+x^2)*(1+18*x+x^2))+O(x^99))
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CROSSREFS
| Cf. A046193, A046194.
Sequence in context: A035320 A200458 A071096 * A127947 A095232 A042209
Adjacent sequences: A039832 A039833 A039834 * A039836 A039837 A039838
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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