A068508 -id:A068508 - cp's OEIS frontend

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

Michael Somos, Jan 27 2012

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

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

Cf. A068508, A185341, A205303.

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 *)

{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] ))};

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

A185341 Denominators of u(n) where u(n) = (u(n-1) + u(n-2)) / u(n-3), with u(1) = u(2) = u(3) = 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 5, 10, 6, 21, 77, 55, 145, 899, 868, 1988, 38411, 90347, 95357, 637807, 3506263, 2382501, 19519203, 649945741, 911672929, 3857971277, 130630182325, 366719420575, 764101349503, 12533062448579, 136235802233249

Offset: 1

Michael Somos, Jan 27 2012

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

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

Cf. A068508, A185332, A205303.

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 *)

{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] ))};

u(4 - n) = u(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

A330080 a(n) = floor(b(n)), where b(1) = b(2) = b(3) = 1 and b(n) = (b(n-1) + b(n-2))/b(n-3) for n > 3.

Original entry on oeis.org

1, 1, 1, 2, 3, 5, 4, 3, 1, 1, 0, 1, 2, 4, 4, 4, 2, 1, 0, 1, 1, 2, 3, 5, 3, 2, 1, 1, 0, 1, 2, 4, 4, 3, 1, 1, 0, 1, 1, 3, 4, 4, 2, 1, 0, 1, 1, 2, 3, 5, 3, 2, 1, 1, 0, 1, 2, 4, 4, 3, 1, 1, 0, 1, 1, 3, 4, 4, 2, 1, 0, 1, 1, 2, 3, 5, 3, 2, 1, 1, 0, 1, 2, 4, 4, 3, 1, 1, 0, 1, 1, 3, 4, 4, 2, 1, 0, 1, 1, 2, 3, 5

Offset: 1

Andres Cicuttin, Nov 30 2019

nonn

This sequence seems quasiperiodic with the same quasiperiod of A185332(n)/A185341(n) (see related comments of Michael Somos in A068508).

Conjecture: 0 <= a(n) <= 5.

Cf. A068508, A185332, A185341.

c[1] = 1; c[2] = 1; c[3] = 1;
c[n_] := c[n] = (c[n - 2] + c[n - 1])/c[n - 3];
Table[Floor@c[j], {j, 1, 2^6}]

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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.

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A185341 Denominators of u(n) where u(n) = (u(n-1) + u(n-2)) / u(n-3), with u(1) = u(2) = u(3) = 1.

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A330080 a(n) = floor(b(n)), where b(1) = b(2) = b(3) = 1 and b(n) = (b(n-1) + b(n-2))/b(n-3) for n > 3.

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