A296016 - OEIS

%I #4 Dec 02 2017 21:49:08

%S 6,69,280,1644,10703,58506,341979,2028843,11696474,68225570,398760505,

%T 2319839274,13523201423,78852368243,459434459883,2677820327762,

%U 15608232354908,90964787662250,530173471171647,3090042672857392

%N Number of nX5 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.

%C Column 5 of A296019.

%H R. H. Hardin, <a href="/A296016/b296016.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +8*a(n-2) +151*a(n-3) -114*a(n-4) -515*a(n-5) -8244*a(n-6) +1988*a(n-7) +12138*a(n-8) +228736*a(n-9) -4994*a(n-10) -139826*a(n-11) -3736405*a(n-12) -234969*a(n-13) +933715*a(n-14) +38898983*a(n-15) +3338523*a(n-16) -4871068*a(n-17) -269945306*a(n-18) -22694433*a(n-19) +28796552*a(n-20) +1279507004*a(n-21) +100906358*a(n-22) -161008139*a(n-23) -4188737496*a(n-24) -351536978*a(n-25) +610732726*a(n-26) +9503090118*a(n-27) +1028936246*a(n-28) -1402429362*a(n-29) -14952641505*a(n-30) -2328423899*a(n-31) +1855181758*a(n-32) +16382179532*a(n-33) +3616522481*a(n-34) -1263845957*a(n-35) -12675982607*a(n-36) -3564185179*a(n-37) +196252504*a(n-38) +7067486428*a(n-39) +2167429718*a(n-40) +383587332*a(n-41) -2788913588*a(n-42) -831651808*a(n-43) -387878170*a(n-44) +699906992*a(n-45) +191664536*a(n-46) +157176764*a(n-47) -107779300*a(n-48) -35713212*a(n-49) -28734376*a(n-50) +9295024*a(n-51) +9393808*a(n-52) +3707904*a(n-53) -13440*a(n-54) -952896*a(n-55)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A296019.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 02 2017