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A048904
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Indices of heptagonal numbers (A000566) which are also octagonal.
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3
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1, 345, 166145, 80081401, 38599068993, 18604671173081, 8967412906355905, 4322274416192372985, 2083327301191817422721, 1004159436900039805378393, 484002765258517994374962561, 233288328695168773248926575865
(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)) = (sqrt(5)+sqrt(6))^4 = 241+44*sqrt(30). - Ant King, Dec 30 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Octagonal Heptagonal Number.
Index to sequences with linear recurrences with constant coefficients, signature (483,-483,1).
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FORMULA
| G.f. x*(-1+138*x+7*x^2) / ( (x-1)*(x^2-482*x+1) ). - R. J. Mathar, Dec 21 2011
Contribution from Ant King, Dec 30 2011: (Start)
a(n) = 482*a(n-1)-a(n-2)-144.
a(n) = 1/60*((3*sqrt(5)+sqrt(6))*(sqrt(5)+sqrt(6))^(4n-3)+ (3*sqrt(5)-sqrt(6))*(sqrt(5)-sqrt(6))^(4n-3)+18).
a(n) = ceiling(1/60*(3*sqrt(5)+sqrt(6))*(sqrt(5)+sqrt(6))^(4n-3)). (End)
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MATHEMATICA
| LinearRecurrence[{483, -483, 1}, {1, 345, 166145}, 30]
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PROG
| (MAGMA) I:=[1, 345, 166145]; [n le 3 select I[n] else 483*Self(n-1)-483*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Dec 28 2011
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CROSSREFS
| Cf. A048905, A048906.
Sequence in context: A063370 A095963 A138043 * A139266 A063536 A045102
Adjacent sequences: A048901 A048902 A048903 * A048905 A048906 A048907
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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