A205303 -id:A205303 - 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

A068508 a(n) = round((a(n-1) + a(n-2))/a(n-3)) starting with a(1)=a(2)=a(3)=1.

Original entry on oeis.org

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

Offset: 1

Henry Bottomley, Mar 25 2002

While this sequence has period 8, the unrounded version b(n) = (b(n-1) + b(n-2))/b(n-3) seems to have a quasi-period of about 8.7 for this particular starting point.

The unrounded version b(n) = A185332(n) / A185341(n) as given in A205303 has 8.694171... quasi-period. - Michael Somos, Oct 22 2018

			a(7) = round((a(6) + a(5))/a(4)) = round((5+3)/2) = 4.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Cf. A048112, A185332, A185341, A205303.

a(n) = a(n-8).

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A068508 a(n) = round((a(n-1) + a(n-2))/a(n-3)) starting with a(1)=a(2)=a(3)=1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula