A299309 - OEIS

%I #4 Feb 06 2018 13:35:08

%S 1,7,15,29,63,199,593,1657,4689,13395,38357,109855,313667,896417,

%T 2563517,7330205,20956899,59914557,171302635,489779503,1400327457,

%U 4003663145,11446878297,32727841823,93572301793,267532776375,764903730599

%N Number of nX3 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Column 3 of A299314.

%H R. H. Hardin, <a href="/A299309/b299309.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) -3*a(n-4) -6*a(n-5) -8*a(n-6) +18*a(n-7) +27*a(n-8) -18*a(n-9) +15*a(n-10) -55*a(n-11) +21*a(n-12) -6*a(n-13) +14*a(n-14) +2*a(n-15) -2*a(n-16) for n>17

%e Some solutions for n=6

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

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

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

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

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

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

%Y Cf. A299314.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 06 2018