

A133129


Number of black/white colorings of a 3 X n rectangle which have no monochromatic 2 by 2 subsquares.


3



1, 8, 50, 322, 2066, 13262, 85126, 546410, 3507314, 22512862, 144506294, 927561722, 5953863490, 38216853518, 245307588134, 1574588362378, 10107019231634, 64875265300670, 416423472774166, 2672952594083738, 17157235452223586, 110129423550044398
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000


FORMULA

G.f.: 1+x*(8+2*x2*x^2)/(16*x3*x^2+2*x^3).  Colin Barker, Jan 04 2012


EXAMPLE

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.


CROSSREFS

Cf. A055099, A133357.
Column k=3 of A181245.
Sequence in context: A240050 A221478 A180029 * A103458 A238841 A100310
Adjacent sequences: A133126 A133127 A133128 * A133130 A133131 A133132


KEYWORD

nonn


AUTHOR

Victor S. Miller, Sep 19 2007


EXTENSIONS

More terms from Colin Barker, Jan 03 2012
a(0)=1 prepended and g.f. adapted by Alois P. Heinz, Feb 19 2015


STATUS

approved



