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.

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

Table of n, a(n) for n=0..22.

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]

Index entries for linear recurrences with constant coefficients, signature (7, -7, 1).

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

Cf. A046092, A108261.

Sequence in context: A065914 A288759 A180368 * A034892 A072687 A353718

Adjacent sequences: A108259 A108260 A108261 * A108263 A108264 A108265

Keyword

nonn

Author

Kenneth J Ramsey, May 29 2005

Extensions

More terms from Harvey P. Dale, Mar 15 2011

Status

approved