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

1, 1, 1, 28, 271, 1567, 6616, 21925, 60481, 164836, 627751, 3355183, 18052336, 84393037, 338279761, 1198269100, 4009627711, 14134316671, 57201128776, 256878349813, 1159252365601, 4930744442932, 19479046111831

Offset

0,4

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.: (1-8*x+25*x^2) / ((1-4*x)*(1-5*x+13*x^2)).

(End)

Example

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

Crossrefs

Cf. A065692, A065694.

Sequence in context: A093196 A179098 A223111 * A349861 A159883 A125391

Adjacent sequences: A065690 A065691 A065692 * A065694 A065695 A065696

Keyword

nonn

Author

Henry Bottomley, Nov 14 2001

Status

approved