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A048902
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Indices of heptagonal numbers (A000566) which are also hexagonal.
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3
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1, 221, 71065, 22882613, 7368130225, 2372515049741, 763942477886281, 245987105364332645, 79207083984837225313, 25504435056012222218045, 8212348880951950716985081, 2644350835231472118646977941
(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)) = (2+sqrt(5))^4 = 161+72*sqrt(5). - Ant King, Dec 26 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Heptagonal hexagonal number.
Index to sequences with linear recurrences with constant coefficients, signature (323,-323,1).
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FORMULA
| G.f. -x*(1-102*x+5*x^2) / ( (x-1)*(x^2-322*x+1) ). - R. J. Mathar, Dec 21 2011
Contribution from Ant King, Dec 26 2011: (Start)
a(n) = 322*a(n-1)-a(n-2)-96
a(n) = 1/20*((sqrt(5)+1)*(sqrt(5)+2)^(4n-3)+(sqrt(5)-1)*(sqrt(5)-2)^(4n-3)+6)
a(n) = ceiling(1/20*(sqrt(5)+1)*(sqrt(5)+2)^(4n-3))
(End)
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MATHEMATICA
| LinearRecurrence[{323, -323, 1}, {1, 221, 71065}, 12]; (* Ant King, Dec 26 2011 *)
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PROG
| (MAGMA) I:=[1, 221, 71065]; [n le 3 select I[n] else 323*Self(n-1)-323*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Dec 28 2011
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CROSSREFS
| Cf. A048901, A048903.
Sequence in context: A177422 A177420 A011816 * A013548 A083958 A083959
Adjacent sequences: A048899 A048900 A048901 * A048903 A048904 A048905
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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