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

0, 3, 24, 117, 417, 1140, 2583, 7311, 39840, 251613, 1329969, 5738172, 20838447, 67344735, 216818808, 812592261, 3660235905, 17401156548, 78077421639, 318790895727, 1197423287952, 4316735957805, 15912781695633

Offset

0,2

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..22.

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.: 3*x*(1-x) / ((1-4*x)*(1-5*x+13*x^2)).

(End)

Example

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

Crossrefs

Cf. A065693, A065694.

Sequence in context: A354676 A253944 A139031 * A127520 A175115 A301812

Adjacent sequences: A065689 A065690 A065691 * A065693 A065694 A065695

Keyword

nonn

Author

Henry Bottomley, Nov 14 2001

Status

approved