A072557 -id:A072557 - cp's OEIS frontend

A072560 Denominators of w(n) where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

3, 9, 3, 3, 1, 3, 3, 9, 3, 3, 1, 3, 3, 9, 3, 1, 1, 1, 3, 9, 3, 3, 1, 3, 3, 9, 3, 3, 1, 3, 3, 9, 3, 1, 1, 1, 3, 9, 3, 3, 1, 3, 3, 9, 3, 3, 1, 3, 3, 9, 3, 1, 1, 1, 3, 9, 3, 3, 1, 3, 3, 9, 3, 3, 1, 3, 3, 9, 3, 1, 1, 1, 3, 9, 3, 3, 1, 3, 3, 9, 3, 3, 1, 3, 3, 9, 3, 1, 1, 1, 3, 9, 3, 3, 1, 3, 3, 9, 3, 3, 1, 3, 3, 9, 3

Offset: 1

Benoit Cloitre, Aug 06 2002

Sequence contains 1,3 or 9 only and is periodic with period (3,9,3,3,1,3,3,9,3,3,1,3,3,9,3,1,1,1) of length 18.

			The sequence w() begins: 1, 1, 1, 5/3, 23/9, 17/3, 31/3, 25, 143/3, 353/3, 2039/9, 1685/3, 3251/3, 2689, 15571/3, ...

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

Cf. A072561, A072557.

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{3, 9, 3, 3, 1, 3, 3, 9, 3, 3, 1, 3, 3, 9, 3, 1, 1, 1},105] (* Ray Chandler, Aug 25 2015 *)
PadRight[{},120,{3,9,3,3,1,3,3,9,3,3,1,3,3,9,3,1,1,1}] (* Harvey P. Dale, Apr 04 2022 *)

A072561 Denominators of w(n) equals 3 where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

Original entry on oeis.org

1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 19, 21, 22, 24, 25, 27, 28, 30, 31, 33, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 55, 57, 58, 60, 61, 63, 64, 66, 67, 69, 73, 75, 76, 78, 79, 81, 82, 84, 85, 87, 91, 93, 94, 96, 97, 99, 100, 102, 103, 105, 109, 111, 112, 114, 115, 117, 118

Offset: 1

Benoit Cloitre, Aug 06 2002

nonn

Denominators of w(k) are 1, 3 or 9.

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

Cf. A072560, A072557.

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1},{1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 19},67] (* Ray Chandler, Aug 25 2015 *)

lim n -> infinity a(n)/n = 9/5. sequence contains numbers of form (1+18k), (3+18k), (4+18k), (6+18k), (7+18k), (9+18k), (10+18k), (12+18k), (13+18k), (15+18k) k>=0.

Corrected by Franklin T. Adams-Watters, Oct 25 2006

A072563 9w(n) where : w(1)=w(2)=w(3)=1 w(n)=(w(n-1)w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

Original entry on oeis.org

9, 9, 9, 15, 23, 51, 93, 225, 429, 1059, 2039, 5055, 9753, 24201, 46713, 115935, 223799, 555459, 1072269, 2661345, 5137533, 12751251, 24615383, 61094895, 117939369, 292723209, 565081449, 1402521135, 2707467863, 6719882451

Offset: 1

Benoit Cloitre, Aug 06 2002

nonn

All terms are integers.

Cf. A072881, A072557, A072560, A072561.

lim n -> infinity a(n+1)/a(n) = (1/6) * ( 7 + sqrt(21) ) = 1.93042928249263...

G.f.: x(15x^5+23x^4-39x^3-45x^2+9x+9)/(-x^6+6x^4-6x^2+1).

cp's OEIS Frontend

A072560 Denominators of w(n) where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A072561 Denominators of w(n) equals 3 where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A072563 9w(n) where : w(1)=w(2)=w(3)=1 w(n)=(w(n-1)w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

Views

Author

Keywords

Comments

Crossrefs

Formula

cp's OEIS Frontend

A072560 Denominators of w(n) where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A072561 Denominators of w(n) equals 3 where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A072563 9*w(n) where : w(1)=w(2)=w(3)=1 w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

Views

Author

Keywords

Comments

Crossrefs

Formula

A072563 9w(n) where : w(1)=w(2)=w(3)=1 w(n)=(w(n-1)w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).