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A108262
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.
1
3, 8, 39, 220, 1275, 7424, 43263, 252148, 1469619, 8565560, 49923735, 290976844, 1695937323, 9884647088, 57611945199, 335787024100, 1957110199395, 11406874172264, 66484134834183, 387497934832828, 2258503474162779, 13163522910143840, 76722633986700255
OFFSET
0,1
LINKS
K. J. Ramsey, Recursive Series Problem [Edited by Kenneth J. Ramsey, May 14 2011]
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]
FORMULA
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]
EXAMPLE
a(4) = 1275 as 220*1275 = 280500 is a term of A046092.
MATHEMATICA
Transpose[NestList[{Last[#], 6Last[#]-First[#]-6}&, {3, 8}, 20]][[1]] (* Harvey P. Dale, Mar 15 2011 *)
CROSSREFS
Sequence in context: A065914 A288759 A180368 * A034892 A072687 A353718
KEYWORD
nonn
AUTHOR
Kenneth J Ramsey, May 29 2005
EXTENSIONS
More terms from Harvey P. Dale, Mar 15 2011
STATUS
approved