A185341 - OEIS

%I #28 Jun 29 2017 17:08:30

%S 1,1,1,1,1,1,1,1,5,10,6,21,77,55,145,899,868,1988,38411,90347,95357,

%T 637807,3506263,2382501,19519203,649945741,911672929,3857971277,

%U 130630182325,366719420575,764101349503,12533062448579,136235802233249

%N Denominators of u(n) where u(n) = (u(n-1) + u(n-2)) / u(n-3), with u(1) = u(2) = u(3) = 1.

%H Seiichi Manyama, <a href="/A185341/b185341.txt">Table of n, a(n) for n = 1..262</a>

%F u(4 - n) = u(n) for all n in Z.

%F 0 = u(n) * u(n+3) - u(n+1) - u(n+2) for all n in Z. - _Michael Somos_, Nov 01 2014

%e u(1), ... = 1, 1, 1, 2, 3, 5, 4, 3, 7/5, 11/10, 5/6, 29/21, 155/77, 224/55, 639/145, ...

%t Denominator[RecurrenceTable[{u[1] == u[2] == u[3] == 1, u[n] == (u[n - 1] + u[n - 2])/u[n - 3]}, u, {n, 50}]] (* _G. C. Greubel_, Jun 27 2017 *)

%o (PARI) {u(n) = local(v = [1, 1, 1]); if( n<1, n = 4-n); if( n<4, 1, for( k=4, n, v = [v[2], v[3], (v[2] + v[3]) / v[1]]); denominator( v[3] ))};

%Y Cf. A068508, A185332, A205303.

%K nonn,frac

%O 1,9

%A _Michael Somos_, Jan 27 2012