A207436 - OEIS

%I #12 Nov 09 2018 05:24:21

%S 4,16,36,81,196,484,1225,3136,8100,21025,54756,142884,373321,976144,

%T 2553604,6682225,17489124,45778756,119836809,313714944,821280964,

%U 2150084161,5628900676,14736503236,38580423561,101004467344,264432492900

%N Number of n X 2 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.

%C Column 2 of A207442.

%H R. H. Hardin, <a href="/A207436/b207436.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 6*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) for n > 7.

%F Empirical g.f.: x*(4 - 20*x^2 - 7*x^3 + 24*x^4 + 6*x^5 - 5*x^6) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). - _Colin Barker_, Feb 17 2018

%F Empirical: a(n) = 1 - 2*A033999(n)/5 +2*A000045(n+2) +7*A001906(n+1)/5 -3*A001906(n)/5 for n>1. - _R. J. Mathar_, Nov 09 2018

%e Some solutions for n=4:

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 17 2012