A232337 - OEIS

%I #7 Oct 05 2018 11:03:40

%S 1,16,74,154,628,1470,5530,13906,49150,130108,439834,1208138,3956136,

%T 11159566,35718398,102702256,323381538,942724706,2933702600,

%U 8637532046,26653534886,79035941608,242412919890,722524675274,2206433888880

%N Number of 3 X n 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.

%H R. H. Hardin, <a href="/A232337/b232337.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 7*a(n-2) - 3*a(n-3) + 3*a(n-4) - 7*a(n-5) + 2*a(n-6) - 2*a(n-7) + 2*a(n-8) for n>12.

%F Empirical g.f.: x*(1 + 15*x + 51*x^2 - 29*x^3 + x^4 - 55*x^5 + 14*x^6 - 4*x^7 + 20*x^8 - 2*x^10 - 2*x^11) / (1 - x - 7*x^2 + 3*x^3 - 3*x^4 + 7*x^5 - 2*x^6 + 2*x^7 - 2*x^8). - _Colin Barker_, Oct 05 2018

%e Some solutions for n=7.

%e ..0..1..2..1..0..1..0....1..2..1..2..1..2..1....0..1..2..1..2..1..0

%e ..0..1..2..1..2..1..2....1..2..1..0..1..2..1....0..1..2..1..2..1..2

%e ..0..1..0..1..0..1..2....1..2..1..0..1..0..2....0..1..2..1..0..1..2

%Y Row 3 of A232335.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 22 2013