A300142 - OEIS

%I #4 Feb 26 2018 08:08:42

%S 1,16,18,246,1043,5368,37739,219689,1245482,7870135,47636355,

%T 282097766,1725080678,10469667595,62941560035,381690476085,

%U 2313274299430,13972436055633,84576042864758,512096642082119,3097315708720487

%N Number of nX4 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Column 4 of A300146.

%H R. H. Hardin, <a href="/A300142/b300142.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +10*a(n-2) +90*a(n-3) -294*a(n-4) -1000*a(n-5) -1788*a(n-6) +8408*a(n-7) +19306*a(n-8) +13989*a(n-9) -82811*a(n-10) -186056*a(n-11) -11348*a(n-12) +460563*a(n-13) +742483*a(n-14) -281458*a(n-15) -1785439*a(n-16) -836008*a(n-17) +2523733*a(n-18) +1976018*a(n-19) -2319096*a(n-20) -2899510*a(n-21) +899133*a(n-22) +4429039*a(n-23) -1751184*a(n-24) -2174228*a(n-25) +1243411*a(n-26) -1154919*a(n-27) +1558675*a(n-28) +108867*a(n-29) -1129196*a(n-30) +676303*a(n-31) +410519*a(n-32) +172464*a(n-33) -226281*a(n-34) -319702*a(n-35) +87836*a(n-36) +54124*a(n-37) -16318*a(n-38) -2084*a(n-39) +1232*a(n-40) for n>42

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A300146.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 26 2018