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A048916
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Indices of 9-gonal numbers which are also hexagonal.
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3
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1, 10, 39025, 621946, 2517635809, 40124201194, 162422756519761, 2588572715184730, 10478541711598202305, 166999180107303446986, 676012639819623666961969, 10773785102854001863647034
(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+9*x-25499*x^2+2295*x^3+154*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)-23040.
a(n) = 1/28*(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))+10).
a(n) = ceiling(3/28*(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, 10, 39025, 621946, 2517635809}, 210] (* Vincenzo Librandi, Dec 28 2011 *)
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CROSSREFS
| Cf. A048917, A048918.
Sequence in context: A181017 A055321 A092300 * A055310 A048832 A115673
Adjacent sequences: A048913 A048914 A048915 * A048917 A048918 A048919
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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