A087619 - OEIS

%I #17 Jan 25 2020 02:03:18

%S 2,137,18771,2571764,352350439,48274581907,6613970071698,

%T 906162174404533,124150831863492719,17009570127472907036,

%U 2330435258295651756651,319286639956631763568223

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

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

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

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

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

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

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

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (137,1).

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

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

%F G.f.: (2-137*x)/(1-137*x-x^2). - _Philippe Deléham_, Nov 23 2008

%Y Cf. A037088, A073481.

%K easy,nonn

%O 0,1

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