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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, 387497934832828, 2258503474162779, 13163522910143840, 76722633986700255
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OFFSET
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0,1
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LINKS
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Kenneth J. Ramsey, Recursive Series Problem, digest of 4 messages in Triangular_and_Fibonacci_Numbers Yahoo group, May 28, 2005 - Mar 9, 2006. [Cached copy]
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FORMULA
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a(n) = 6*a(n-1) - a(n-2) - 6.
G.f.: (-4*x^2+13*x-3)/(x^3-7*x^2+7*x-1). [Harvey P. Dale, Mar 15 2011]
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EXAMPLE
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a(4) = 1275 as 220*1275 = 280500 is a term of A046092.
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MATHEMATICA
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Transpose[NestList[{Last[#], 6Last[#]-First[#]-6}&, {3, 8}, 20]][[1]] (* Harvey P. Dale, Mar 15 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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