A298282 - OEIS

%I #8 Feb 26 2018 12:15:36

%S 4,25,70,205,614,1860,5631,17034,51507,155755,471038,1424553,4308225,

%T 13029159,39403450,119165999,360388207,1089905354,3296150132,

%U 9968393611,30146949453,91172018210,275727297765,833869252932,2521832029371

%N Number of n X 3 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

%C Column 3 of A298287.

%H R. H. Hardin, <a href="/A298282/b298282.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - a(n-2) + 2*a(n-3) + 4*a(n-4) - a(n-5) + 2*a(n-6) - 2*a(n-7) - 3*a(n-8) - 2*a(n-9) - 2*a(n-10) - 2*a(n-11) for n>12.

%F Empirical g.f.: x*(4 + 13*x - x^2 + 12*x^3 + 3*x^4 - 13*x^5 - 8*x^6 - 19*x^7 - 13*x^8 - 7*x^9 - 2*x^10 - 4*x^11) / (1 - 3*x + x^2 - 2*x^3 - 4*x^4 + x^5 - 2*x^6 + 2*x^7 + 3*x^8 + 2*x^9 + 2*x^10 + 2*x^11). - _Colin Barker_, Feb 26 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Cf. A298287.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2018