A281884 - OEIS

%I #4 Feb 01 2017 09:22:38

%S 0,0,638,9284,112320,1282388,13907664,146131060,1503637694,

%T 15223224224,152175478036,1505762808388,14774737843360,

%U 143953529386540,1394189557409864,13433205796090216,128850654080499482

%N Number of nX4 0..1 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Column 4 of A281888.

%H R. H. Hardin, <a href="/A281884/b281884.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*a(n-1) -81*a(n-2) +64*a(n-3) -1080*a(n-4) +3812*a(n-5) +4856*a(n-6) +23306*a(n-7) -49388*a(n-8) -196528*a(n-9) -355562*a(n-10) +8698*a(n-11) +1438524*a(n-12) +2402608*a(n-13) +1412125*a(n-14) -4250078*a(n-15) -7306595*a(n-16) -4311988*a(n-17) +6204595*a(n-18) +10484738*a(n-19) -262044*a(n-20) -6382476*a(n-21) -5774611*a(n-22) +15155406*a(n-23) +3345731*a(n-24) -719656*a(n-25) -15801373*a(n-26) +3275002*a(n-27) -1807108*a(n-28) +5097666*a(n-29) -3930752*a(n-30) +1153026*a(n-31) -2585642*a(n-32) +2410196*a(n-33) +1152527*a(n-34) +922528*a(n-35) -1044890*a(n-36) -301404*a(n-37) -95377*a(n-38) +66504*a(n-39) +99340*a(n-40) +40236*a(n-41) -43720*a(n-42) -31520*a(n-43) +16508*a(n-44) +3264*a(n-45) -2304*a(n-46) for n>49

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281888.

%K nonn

%O 1,3

%A _R. H. Hardin_, Feb 01 2017