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A048901
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Indices of hexagonal numbers which are also heptagonal.
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3
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1, 247, 79453, 25583539, 8237820025, 2652552464431, 854113655726677, 275021944591525483, 88556212044815478769, 28514825256485992638055, 9181685176376444813974861, 2956474111967958744107267107
(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 24 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+76*x+5*x^2) / ( (x-1)*(x^2-322*x+1) ). - R. J. Mathar, Dec 21 2011
Contribution from Ant King, Dec 24 2011: (Start)
a(n) = 322*a(n-1)-a(n-2)-80.
a(n) = 1/40*sqrt(5)*((1+sqrt(5))*(sqrt(5)+2)^(4n-3)+(1-sqrt(5))*(sqrt(5)-2)^(4n-3)+2*sqrt(5)).
a(n) = ceiling(1/40*sqrt(5)*(1+sqrt(5))*(sqrt(5)+2)^(4n-3)).
(End)
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MATHEMATICA
| LinearRecurrence[{323, -323, 1}, {1, 247, 79453}, 12]; (* Ant King, Dec 24 2011 *)
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PROG
| (MAGMA) I:=[1, 247, 79453]; [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. A048902, A048903.
Sequence in context: A166399 A129133 A001243 * A187398 A065146 A064977
Adjacent sequences: A048898 A048899 A048900 * A048902 A048903 A048904
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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