A065694 Braided power sequence: A065692 is b(n+1)=3b(n)+2d(n)-c(n), A065693 is c(n+1)=3c(n)+2b(n)-d(n) and this is d(n+1)=3d(n)+2c(n)-b(n), starting with b(0)=0, c(0)=1 and d(0)=2.

2, 8, 23, 47, 80, 365, 3089, 19916, 96287, 369983, 1188008, 3489557, 11440865, 49588820, 250207799, 1210364111, 5215038272, 20004134333, 70879879793, 248964475292, 941859229775, 3946659132575, 17384730325784, 75199501505381

Offset

0,1

Comments

Tends to 4^n. "Braided" because the order of b(n), c(n) and d(n) changes between the six possibilities as n increases.

Links

Table of n, a(n) for n=0..23.

Formula

Conjectures from Colin Barker, Sep 02 2016: (Start)

a(n) = 9*a(n-1)-33*a(n-2)+52*a(n-3) for n>2.

G.f.: (2-10*x+17*x^2) / ((1-4*x)*(1-5*x+13*x^2)).

(End)

Example

a(1) = 3*2+2*1-1*0 = 8.

Crossrefs

Cf. A065692, A065693.

Sequence in context: A303287 A321068 A158466 * A178129 A203298 A161463

Adjacent sequences: A065691 A065692 A065693 * A065695 A065696 A065697

Keyword

nonn

Author

Henry Bottomley, Nov 14 2001

Status

approved