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A048919
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Indices of 9-gonal numbers which are also heptagonal.
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4
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1, 88, 12445, 1767052, 250908889, 35627295136, 5058825000373, 718317522757780, 101996029406604337, 14482717858215058024, 2056443939837131635021, 292000556739014477114908
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| As n increases, this sequence is approximately geometric with common ratio r = lim(n->Infinity,a(n)/a(n-1)) = (6+sqrt(35))^2 = 71+12*sqrt(35). - Ant King, Jan 01 2012
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Nonagonal Heptagonal number.
Index to sequences with linear recurrences with constant coefficients, signature (143,-143,1).
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FORMULA
| G.f. -x*(1-55*x+4*x^2) / ( (x-1)*(x^2-142*x+1) ). - R. J. Mathar, Dec 21 2011
a(n) = (50+(25-3r)*(6+r)^(2n-1)+(25+3r)*(6-r)^(2n-1))/140, where r=sqrt(35). - Bruno Berselli, Dec 21 2011
Contribution from Ant King, Jan 01 2012: (Start)
a(n) = 142*a(n-1)-a(n-2)-50.
a(n)=ceiling(1/140*(45+7*sqrt(35))*(6+sqrt(35))^(2*n-2)). (End)
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MATHEMATICA
| LinearRecurrence[{143, -143, 1}, {1, 88, 12445}, 30] (* Vincenzo Librandi, Dec 21 2011 *)
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PROG
| (MAGMA) I:=[1, 88, 12445]; [n le 3 select I[n] else 143*Self(n-1)-143*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 21 2011
(Maxima) makelist(expand((50+(25-3*sqrt(35))*(6+sqrt(35))^(2*n-1)+(25+3*sqrt(35))*(6-sqrt(35))^(2*n-1))/140), n, 1, 12); [Bruno Berselli, Dec 21 2011]
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CROSSREFS
| Cf. A048920, A048921.
Sequence in context: A189201 A052069 A174499 * A159718 A157460 A093244
Adjacent sequences: A048916 A048917 A048918 * A048920 A048921 A048922
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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