A298722 - OEIS

%I #4 Jan 25 2018 08:54:39

%S 1,7,5,15,21,57,119,285,725,1833,4807,12843,34439,93327,254085,693267,

%T 1896489,5194309,14237415,39049277,107136761,294009425,806965323,

%U 2215076227,6080649203,16692824711,45826947389,125811287255,345400728813

%N Number of nX3 0..1 arrays with every element equal to 0, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

%C Column 3 of A298727.

%H R. H. Hardin, <a href="/A298722/b298722.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -5*a(n-2) -5*a(n-3) -2*a(n-4) +18*a(n-5) +14*a(n-6) -30*a(n-7) -8*a(n-8) -22*a(n-9) +4*a(n-10) +84*a(n-11) +3*a(n-12) -33*a(n-13) -9*a(n-14) -21*a(n-15) +4*a(n-16) +4*a(n-17) for n>18

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A298727.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 25 2018