A133129 Number of black/white colorings of a 3 X n rectangle which have no monochromatic 2 by 2 subsquares.
1, 8, 50, 322, 2066, 13262, 85126, 546410, 3507314, 22512862, 144506294, 927561722, 5953863490, 38216853518, 245307588134, 1574588362378, 10107019231634, 64875265300670, 416423472774166, 2672952594083738, 17157235452223586, 110129423550044398
Offset: 0
Keywords
Examples
a(2) = 50 because if the middle row is not monochromatic, the top and bottom rows are unconstrained, contributing 2*4*4. if the middle row is monochromatic, the top and bottom rows can each take on only 3 values contributing 2*3*3.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6, 3, -2).
Formula
G.f.: 1+x*(8+2*x-2*x^2)/(1-6*x-3*x^2+2*x^3). - Colin Barker, Jan 04 2012
Extensions
More terms from Colin Barker, Jan 03 2012
a(0)=1 prepended and g.f. adapted by Alois P. Heinz, Feb 19 2015