A305645 - OEIS

%I #4 Jun 07 2018 09:07:10

%S 5,21,31,137,574,2360,13498,83190,481377,2919477,18188505,111190231,

%T 681420231,4209030021,25916430566,159406198332,982241553059,

%U 6051046080917,37258819107772,229490403681192,1413605674151764

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

%C Column 4 of A305649.

%H R. H. Hardin, <a href="/A305645/b305645.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) -53*a(n-2) +208*a(n-3) -1025*a(n-4) +3124*a(n-5) -6614*a(n-6) +20019*a(n-7) -52896*a(n-8) +95825*a(n-9) -213582*a(n-10) +452071*a(n-11) -722917*a(n-12) +1317805*a(n-13) -2044503*a(n-14) +2703274*a(n-15) -4185687*a(n-16) +4037722*a(n-17) -3566939*a(n-18) +2631534*a(n-19) +6295616*a(n-20) -11042762*a(n-21) +24218324*a(n-22) -54093882*a(n-23) +63608167*a(n-24) -77176201*a(n-25) +118700537*a(n-26) -166637364*a(n-27) +138057125*a(n-28) -110211186*a(n-29) +164465821*a(n-30) -107581221*a(n-31) +147189359*a(n-32) -69901128*a(n-33) -233098157*a(n-34) +37858384*a(n-35) +6891596*a(n-36) +250149252*a(n-37) -131157175*a(n-38) +122684063*a(n-39) -39643231*a(n-40) -101368179*a(n-41) -102287871*a(n-42) -94827300*a(n-43) +50798280*a(n-44) +27596612*a(n-45) +23871896*a(n-46) +11304776*a(n-47) +4047152*a(n-48) +902752*a(n-49) -175152*a(n-50) +240928*a(n-51) -119104*a(n-52) +7552*a(n-53) +2560*a(n-54) for n>57

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A305649.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 07 2018