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A300205 Number of n X 5 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%I A300205 #6 Mar 24 2023 10:02:06
%S A300205 16,512,15070,451996,13548425,406228452,12180207076,365209429387,
%T A300205 10950385677546,328334797496128,9844743765773028,295183394744945449,
%U A300205 8850736864575395877,265379233550361130727,7957093141320853026332
%N A300205 Number of n X 5 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C A300205 Column 5 of A300208.
%H A300205 R. H. Hardin, <a href="/A300205/b300205.txt">Table of n, a(n) for n = 1..210</a>
%F A300205 Empirical: a(n) = 30*a(n-1) -8*a(n-2) +343*a(n-3) -3214*a(n-4) -9170*a(n-5) -6989*a(n-6) -9332*a(n-7) +482996*a(n-8) +36160*a(n-9) +495066*a(n-10) -4606283*a(n-11) -2769327*a(n-12) +1332664*a(n-13) +25229638*a(n-14) +18945541*a(n-15) -24172763*a(n-16) -111255521*a(n-17) -63862029*a(n-18) +129871861*a(n-19) +300380879*a(n-20) +152885144*a(n-21) -339369704*a(n-22) -486006309*a(n-23) -128959877*a(n-24) +341481538*a(n-25) +413606386*a(n-26) +91315190*a(n-27) -187554462*a(n-28) -184211455*a(n-29) -33354181*a(n-30) +50022664*a(n-31) +38893772*a(n-32) +6506118*a(n-33) -4777876*a(n-34) -3960944*a(n-35) -936320*a(n-36) +381696*a(n-37) +156672*a(n-38).
%e A300205 Some solutions for n=5
%e A300205 ..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0
%e A300205 ..0..0..1..0..0. .0..0..0..1..1. .0..0..0..0..0. .0..0..1..0..1
%e A300205 ..0..1..1..0..1. .0..1..1..1..0. .0..1..1..1..0. .0..1..1..1..0
%e A300205 ..0..1..0..1..0. .1..1..0..0..0. .1..0..1..0..0. .1..0..1..0..1
%e A300205 ..0..1..1..0..0. .0..1..0..1..1. .1..1..0..0..1. .1..1..0..0..1
%Y A300205 Cf. A300208.
%K A300205 nonn
%O A300205 1,1
%A A300205 _R. H. Hardin_, Feb 28 2018