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A048907
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Indices of 9-gonal numbers which are also triangular.
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3
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1, 10, 154, 2449, 39025, 621946, 9912106, 157971745, 2517635809, 40124201194, 639469583290, 10191389131441, 162422756519761, 2588572715184730, 41254740686435914, 657487278267789889, 10478541711598202305
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Entries are == 1 (mod 3). - N. J. A. Sloane (njas(AT)research.att.com), Sep 22, 2007
lim(n -> Infinity, a(n)/a(n-1)) = 8 + 3*sqrt(7) . - Ant King, Nov 03 2011
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| G.f.: [1-7x+x^2]/[(1-x)(1-16x+x^2)].
a(n+2)=16*a(n+1)-a(n)-5, a(n+1)=8*a(n)-2.5+1.5*(28*a(n)^2-20*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 22 2007
a(n)=(5/14)+(9/28)*{[8-3*sqrt(7)]^n+[8+3*sqrt(7)]^n}+(3/28)*sqrt(7)*{[8+3*sqrt(7)]^n- [8-3*sqrt(7)]^n}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 25 2008]
From Ant King, Nov 03 2011: (Start)
a(n) = 17*a(n-1) - 17*a(n-2) + a(n-3).
a(n) = ceiling(3/28*(3-sqrt(7))*(8 + 3*sqrt(7))^n).
(End)
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MATHEMATICA
| LinearRecurrence[{17, -17, 1}, {1, 10, 154}, 17]; (* Ant King, Nov 03 2011 *)
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CROSSREFS
| Cf. A001080, A073352, A048908, A048909.
Sequence in context: A025750 A034325 A178298 * A061654 A087603 A129460
Adjacent sequences: A048904 A048905 A048906 * A048908 A048909 A048910
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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