A087619 a(n) = 137*a(n-1) + a(n-2), with a(0) = 2 and a(1) = 137.

2, 137, 18771, 2571764, 352350439, 48274581907, 6613970071698, 906162174404533, 124150831863492719, 17009570127472907036, 2330435258295651756651, 319286639956631763568223, 43744600109316847260603202, 5993329501616364706466206897, 821129886321551281633130948091

Offset

0,1

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (137,1).

Formula

a(n) = ((137+sqrt(18773))/2)^n + ((137-sqrt(18773))/2)^n.

a(n+1)/a(n) converges to (137+sqrt(18773))/2 = 137.00729888121410965...

Limit_{n->infinity} a(n)/a(n+1) = 0.00729888121410965... = 2/(137+sqrt(18773)) = (sqrt(18773)-137)/2.

(a(n))^2 = a(2*n)-2 if n = 1, 3, 5, ..., (a(n))^2 = a(2n) + 2 if n = 2, 4, 6, ...

G.f.: (2-137*x)/(1-137*x-x^2). - Philippe Deléham, Nov 23 2008

Crossrefs

Sequence in context: A139907 A195379 A221227 * A157072 A051029 A212715

Adjacent sequences: A087616 A087617 A087618 * A087620 A087621 A087622

Keyword

easy,nonn

Author

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 25 2003

Extensions

a(12) onward from Andrew Howroyd, Nov 08 2025

Status

approved