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%I #6 Dec 26 2023 18:08:04
%S 8,29,27,41,101,158,263,481,776,1387,2567,4539,8077,14329,25589,46648,
%T 84839,153497,278093,503244,917222,1678100,3060188,5584638,10197411,
%U 18619047,34091728,62438325,114225230,209134304,382969204,701383579
%N Number of n X 4 0..1 arrays with every element equal to 0, 1, 2, 4 or 7 king-move adjacent elements, with upper left element zero.
%C Column 4 of A298494.
%H R. H. Hardin, <a href="/A298490/b298490.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +a(n-2) +6*a(n-3) -14*a(n-4) -8*a(n-5) -12*a(n-6) +16*a(n-7) +24*a(n-8) +27*a(n-9) +102*a(n-10) +13*a(n-11) -99*a(n-12) -390*a(n-13) -297*a(n-14) +126*a(n-15) +559*a(n-16) +781*a(n-17) +129*a(n-18) -240*a(n-19) -723*a(n-20) -356*a(n-21) -201*a(n-22) -117*a(n-23) +59*a(n-24) -69*a(n-25) +401*a(n-26) +250*a(n-27) +595*a(n-28) +310*a(n-29) +46*a(n-30) -311*a(n-31) -636*a(n-32) -423*a(n-33) -181*a(n-34) +315*a(n-35) +344*a(n-36) +144*a(n-37) -84*a(n-38) -96*a(n-39) -12*a(n-40) +20*a(n-41) for n>43.
%e Some solutions for n=9
%e ..0..0..1..0. .0..0..1..0. .0..0..1..1. .0..0..1..0. .0..0..1..1
%e ..1..1..0..1. .1..1..0..1. .1..1..0..0. .1..1..0..0. .1..0..1..0
%e ..1..0..1..0. .0..0..0..1. .0..1..1..1. .1..0..1..1. .0..1..0..1
%e ..1..1..1..0. .1..0..1..0. .0..1..0..0. .0..0..0..0. .1..0..1..0
%e ..1..1..1..0. .1..0..1..0. .0..1..1..1. .1..1..0..1. .0..1..0..1
%e ..1..0..1..0. .1..0..1..0. .1..0..1..0. .0..0..1..1. .1..0..1..0
%e ..0..0..1..1. .0..1..1..1. .1..0..1..0. .0..1..0..0. .0..1..0..1
%e ..0..0..1..1. .0..1..0..0. .0..0..0..1. .0..0..0..1. .1..0..1..0
%e ..1..0..1..0. .1..0..1..1. .1..1..0..1. .1..1..1..0. .0..1..0..1
%Y Cf. A298494.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 20 2018
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