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A048920
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Indices of heptagonal numbers (A000566) which are also 9-gonal.
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6
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1, 104, 14725, 2090804, 296879401, 42154784096, 5985682462189, 849924754846700, 120683329505769169, 17136182865064375256, 2433217283509635517141, 345499718075503179058724
(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, Dec 31 2011
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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
| Contribution from Bruno Berselli, Dec 20 2011: (Start)
G.f.: x*(1-39*x-4*x^2)/((1-x)*(1-142*x+x^2)).
a(n) = (42+(-21+5r)*(6+r)^(2n-1)-(21+5r)*(6-r)^(2n-1))/140, where r=sqrt(35). (End)
Contribution from Ant King, Dec 31 2011: (Start)
a(n) = 142*a(n-1)-a(n-2)-42.
a(n) = ceiling(1/140*(49+9*sqrt(35))*(6+sqrt(35))^(2*n-2)).
(End)
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MATHEMATICA
| LinearRecurrence[{143, -143, 1}, {1, 104, 14725}, 30] (* Vincenzo Librandi, Dec 21 2011 *)
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PROG
| (Maxima) makelist(expand((42+(-21+5*sqrt(35))*(6+sqrt(35))^(2*n-1)-(21+5*sqrt(35))*(6-sqrt(35))^(2*n-1))/140), n, 1, 12); [Bruno Berselli, Dec 20 2011]
(MAGMA) I:=[1, 104, 14725]; [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
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CROSSREFS
| Cf. A000566, A048919, A048921.
Sequence in context: A206013 A187700 A015272 * A091539 A157874 A069172
Adjacent sequences: A048917 A048918 A048919 * A048921 A048922 A048923
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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