OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (10,-8,-80,128).
FORMULA
a(n) = (1/6)*(2^(3*(n-1))+2^n+3*2^(floor((3*n-1)/2))) for n>1.
a(2)=4, a(3)=20, a(4)=104, a(5)=752, a(n)=10*a(n-1)-8*a(n-2)- 80*a(n-3)+ 128*a(n-4). - Harvey P. Dale, Apr 22 2013
G.f.: -x*(64*x^4+16*x^3-12*x^2-6*x+1) / ((2*x-1)*(8*x-1)*(8*x^2-1)). - Colin Barker, Mar 17 2015
EXAMPLE
a(2) = 4, the labelings being {000}, {001}, {011}, {111}. Some of the 20 solutions for n=3 are as follows:
..0......1.......0......1.......1.......1.......0
.0.0....0.0.....1.0....1.0.....0.0.....0.0.....1.1
0.0.0..0.0.0...0.0.0..0.0.0...1.0.0...0.1.0...0.0.0
The first solution for n = 4 is
...0
..0.0
.0...0
0.0.0.0
MATHEMATICA
Join[{1}, Table[((2^(3(n-1)))+2^n+3*2^Floor[(3n-1)/2])/6, {n, 2, 30}]] (* or *) Join[{1}, LinearRecurrence[{10, -8, -80, 128}, {4, 20, 104, 752}, 30]] (* Harvey P. Dale, Apr 22 2013 *)
PROG
(PARI) Vec(-x*(64*x^4+16*x^3-12*x^2-6*x+1)/((2*x-1)*(8*x-1)*(8*x^2-1)) + O(x^100)) \\ Colin Barker, Mar 17 2015
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jun 20 2001
STATUS
approved