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).

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

1,2

Comments

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

Links

Table of n, a(n) for n=1..67.

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

Formula

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.

Mathematica

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 *)

Crossrefs

Cf. A072560, A072557.

Sequence in context: A059559 A329847 A103877 * A330176 A141206 A140100

Adjacent sequences: A072558 A072559 A072560 * A072562 A072563 A072564

Keyword

nonn

Author

Benoit Cloitre, Aug 06 2002

Extensions

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

Status

approved