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.

1, 1, 1, 2, 3, 5, 4, 3, 7, 11, 5, 29, 155, 224, 639, 3787, 1837, 2855, 32393, 97309, 127512, 1825907, 13672693, 12048382, 61067879, 1364331725, 942450221, 3863275086, 126646632559, 699156998051, 2194555785960, 61774183992421

Offset: 1

Author

Michael Somos, Jan 27 2012

Keywords

• nonn
• frac

Examples

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..262

Crossrefs

Cf. A068508, A185341, A205303.

Programs

Mathematica

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 *)

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] ))};

Formula

a(4 - n) = a(n) for all n in Z.

0 = u(n) * u(n+3) - u(n+1) - u(n+2) for all n in Z. - Michael Somos, Nov 01 2014