OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (15,-58,16).
FORMULA
G.f.: x*(1+2*x)/((1-8*x)*(2*x^2-7*x+1)). - Vladeta Jovovic, Jul 02 2003
From Maksym Voznyy (voznyy(AT)mail.ru), Jul 25 2008: (Start)
a(n) = 15*a(n-1) - 58*a(n-2) + 16*a(n-3), where a(1)=1, a(2)=17, a(3)=197;
a(n) = 8^n + 1/sqrt(41)*4^(n+1)*((7+sqrt(41))^(-(n+1)) - (7-sqrt(41))^(-(n+1))). (End)
a(n) = 8^n - A186446(n). - R. J. Mathar, Jan 27 2020
EXAMPLE
The 17 binary arrays for n=2:
01 10 01 10 01 10 01 10 01 10 11 11 11 11 11 11 11
01 10 01 10 11 11 11 11 11 11 01 10 01 01 11 11 11
01 10 11 11 01 10 10 01 11 11 01 10 11 11 01 10 11 - R. J. Mathar, Jun 21 2023
MATHEMATICA
CoefficientList[Series[(-2 z - 1)/(16 z^3 - 58 z^2 + 15 z - 1), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 24 2011 *)
PROG
(PARI) x='x+O('x^30); Vec(x*(1+2*x)/((1-8*x)*(2*x^2-7*x+1))) \\ G. C. Greubel, Apr 22 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Mar 22 2002
STATUS
approved