A183435 - OEIS

A183435

Number of n X 2 binary arrays with every 1 having exactly one king-move neighbor equal to 1.

%I #12 Feb 28 2018 03:12:38

%S 2,7,13,28,69,149,330,755,1681,3756,8457,18937,42418,95183,213349,

%T 478204,1072285,2403885,5388986,12082011,27086537,60724492,136139073,

%U 305209713,684246754,1534012759,3439098365,7710098140,17285247541,38751739141

%N Number of n X 2 binary arrays with every 1 having exactly one king-move neighbor equal to 1.

%C Column 2 of A183442.

%H R. H. Hardin, <a href="/A183435/b183435.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) + a(n-2) + 4*a(n-3).

%F Empirical g.f.: x*(2 + 5*x + 4*x^2) / (1 - x - x^2 - 4*x^3). - _Colin Barker_, Feb 27 2018

%e Some solutions for 3 X 2:

%e 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0

%e 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0

%e 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1

%Y Cf. A183442.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 04 2011