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A108262
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Second order recursive series having the property that the product of any two adjacent terms equals 4 times a triangular number. That is a(n)*a(n+1)= 4*T(c) = 2c(c+1), where c = the term a(n+1) of related series A108261.
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1
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3, 8, 39, 220, 1275, 7424, 43263, 252148, 1469619, 8565560, 49923735, 290976844, 1695937323, 9884647088, 57611945199, 335787024100, 1957110199395, 11406874172264, 66484134834183
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| K. J. Ramsey, RecursiveSeriesProblem [Edited by Kenneth J. Ramsey, May 14 2011]
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FORMULA
| a(n) = 6*a(n-1) - a(n-2) -6
a(n)= 3/2+(1/4)*[3+2*sqrt(2)]^n+(1/4)*[3-2*sqrt(2)]^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 25 2008
G.f.: (-4*x^2+13*x-3)/(x^3-7*x^2+7*x-1) [From Harvey P. Dale, Mar 15 2011]
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EXAMPLE
| a(5)=1275
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MATHEMATICA
| Transpose[NestList[{Last[#], 6Last[#]-First[#]-6}&, {3, 8}, 20]][[1]] (* From Harvey P. Dale, Mar 15 2011 *)
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CROSSREFS
| Cf. A108261.
Sequence in context: A106558 A065914 A180368 * A034892 A072687 A110561
Adjacent sequences: A108259 A108260 A108261 * A108263 A108264 A108265
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KEYWORD
| nonn
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AUTHOR
| Kenneth John Ramsey (RamseyKK2(AT)aol.com), May 29 2005
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EXTENSIONS
| More terms from Harvey P. Dale, Mar 15 2011.
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