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

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

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

a(0)/a(1) = 2/137;

a(1)/a(2) = 137/18771;

a(2)/a(3) = 18771/2571764;

a(3)/a(4) = 2571764/352350439; ... etc.

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

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (137,1).

Crossrefs

Cf. A037088, A073481.

Formula

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

(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