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A185332 Numerators of u(n) where u(n) = (u(n-1) + u(n-2)) / u(n-3), with u(1) = u(2) = u(3) = 1. 4

%I

%S 1,1,1,2,3,5,4,3,7,11,5,29,155,224,639,3787,1837,2855,32393,97309,

%T 127512,1825907,13672693,12048382,61067879,1364331725,942450221,

%U 3863275086,126646632559,699156998051,2194555785960,61774183992421

%N Numerators 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="/A185332/b185332.txt">Table of n, a(n) for n = 1..262</a>

%F a(4 - n) = a(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 Numerator[RecurrenceTable[{a[1]==a[2]==a[3]==1,a[n]==(a[n-1]+a[n-2])/ a[n-3]}, a,{n,40}]] (* _Harvey P. Dale_, Jan 28 2013 *)

%o (PARI) {a(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]]); numerator( v[3] ))};

%Y Cf. A068508, A185341, A205303.

%K nonn,frac

%O 1,4

%A _Michael Somos_, Jan 27 2012

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)