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A048917
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Indices of hexagonal numbers which are also 9-gonal.
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3
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1, 13, 51625, 822757, 3330519121, 53079328957, 214865110504441, 3424359827493013, 13861807735752971425, 220919149857804895597, 894280664049502087991881, 14252378030502065207035717
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| As n increases, the ratio of consecutive terms settles into an approximate 2-cycle with the ratio a(n)/a(n-1) bounded above and below by 2024+765*sqrt(7) and 8+3*sqrt(7) respectively. - Ant King, Dec 29 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Nonagonal Hexagonal Number.
Index to sequences with linear recurrences with constant coefficients, signature (1,64514,-64514,-1,1).
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FORMULA
| G.f. x*(-1-12*x+12902*x^2+3036*x^3+203*x^4) / ( (x-1)*(x^2-254*x+1)*(x^2+254*x+1) ). - R. J. Mathar, Dec 21 2011
Contribution from Ant King, Dec 29 2011: (Start)
a(n) = 64514*a(n-2)-a(n-4)-16128.
a(n) = 1/56*sqrt(7)*(3*((3-sqrt(7)*(-1)^n)*(8+3*sqrt(7))^(2*n-2)-(3+sqrt(7)*(-1)^n)*(8-3*sqrt(7))^(2*n-2))+2*sqrt(7)).
a(n) = ceiling(3/56*sqrt(7)*(3-sqrt(7)*(-1)^n)*(8+3*sqrt(7))^(2*n-2)).
(End)
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MATHEMATICA
| LinearRecurrence[{1, 64514, -64514, -1, 1}, {1, 13, 51625, 822757, 3330519121}, 210] (*Vincenzo Librandi, Dec 27 2011 *)
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CROSSREFS
| Cf. A048916, A048918.
Sequence in context: A013752 A076811 A203691 * A081317 A027680 A203675
Adjacent sequences: A048914 A048915 A048916 * A048918 A048919 A048920
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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