A065694 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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)