A065693 Braided power sequence: A065692 is b(n+1) = 3*b(n) + 2*d(n) - c(n), this is c(n+1) = 3*c(n) + 2*b(n) - d(n) and A065694 is d(n+1) = 3*d(n) + 2*c(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, 72877971400975, 269491931950816, 1033364729140381

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

Andrew Howroyd, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (9,-33,52).

Formula

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.

Prog

(PARI) a(n) = {[0, 1, 0]*[3, -1, 2; 2, 3, -1; -1, 2, 3]^n*[0, 1, 2]~} \\ Andrew Howroyd, Dec 29 2024

Crossrefs

Cf. A065692, A065694.

Sequence in context: A093196 A179098 A223111 * A349861 A159883 A125391

Adjacent sequences: A065690 A065691 A065692 * A065694 A065695 A065696

Keyword

nonn,easy

Author

Henry Bottomley, Nov 14 2001

Extensions

a(23) onwards from Andrew Howroyd, Dec 29 2024

Status

approved