A298164 - OEIS

%I #6 Jan 15 2022 22:27:00

%S 0,3,3,6,10,18,32,80,171,528,1439,4889,15449,53949,182180,637755,

%T 2204512,7715118,26867102,93989058,328149079,1147549260,4010085072,

%U 14021225991,49011288024,171356237471,599040489814,2094336965494,7321826414980

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

%C Column 5 of A298167.

%H R. H. Hardin, <a href="/A298164/b298164.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +11*a(n-2) -23*a(n-3) -63*a(n-4) +38*a(n-5) +294*a(n-6) +37*a(n-7) -1002*a(n-8) +36*a(n-9) +2280*a(n-10) -608*a(n-11) -3730*a(n-12) +119*a(n-13) +5320*a(n-14) +4302*a(n-15) -7171*a(n-16) -13410*a(n-17) +6800*a(n-18) +28234*a(n-19) +815*a(n-20) -54073*a(n-21) -10366*a(n-22) +86948*a(n-23) +4709*a(n-24) -108386*a(n-25) +16156*a(n-26) +116955*a(n-27) -33161*a(n-28) -124987*a(n-29) +40940*a(n-30) +132629*a(n-31) -62606*a(n-32) -115911*a(n-33) +95342*a(n-34) +85712*a(n-35) -144819*a(n-36) -105111*a(n-37) +216302*a(n-38) +160234*a(n-39) -200504*a(n-40) -180984*a(n-41) +8541*a(n-42) +224078*a(n-43) +219299*a(n-44) -322041*a(n-45) -229238*a(n-46) +296497*a(n-47) +68426*a(n-48) -149490*a(n-49) +38540*a(n-50) +21468*a(n-51) -25611*a(n-52) +28803*a(n-53) -9090*a(n-54) -6735*a(n-55) +1864*a(n-56) -1716*a(n-57) +2058*a(n-58) -1281*a(n-59) -1710*a(n-60) -102*a(n-61) +264*a(n-62) -12*a(n-63) -100*a(n-64) +20*a(n-65) +28*a(n-66) +4*a(n-67).

%e Some solutions for n=8

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

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

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

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

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

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

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

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

%Y Cf. A298167.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 14 2018