A065694 Braided power sequence: A065692 is b(n+1) = 3*b(n) + 2*d(n) - c(n), A065693 is c(n+1) = 3*c(n) + 2*b(n) - d(n) and this is d(n+1) = 3*d(n) + 2*c(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, 308325687691457, 1197353616486308

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

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.: (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.

Prog

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

Crossrefs

Cf. A065692, A065693.

Sequence in context: A303287 A321068 A158466 * A178129 A203298 A161463

Adjacent sequences: A065691 A065692 A065693 * A065695 A065696 A065697

Keyword

nonn,easy

Author

Henry Bottomley, Nov 14 2001

Extensions

a(24) onwards from Andrew Howroyd, Dec 29 2024

Status

approved