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A304006 Number of n X 4 0..1 arrays with every element unequal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

%I A304006 #6 Jan 03 2024 22:12:34
%S A304006 1,13,21,26,64,115,211,439,870,1725,3513,7141,14372,29438,60518,
%T A304006 123439,253860,523477,1075787,2216143,4575316,9438222,19480290,
%U A304006 40253428,83178619,171897255,355448881,735100437,1520380599,3145360038,6508033432
%N A304006 Number of n X 4 0..1 arrays with every element unequal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.
%C A304006 Column 4 of A304010.
%H A304006 R. H. Hardin, <a href="/A304006/b304006.txt">Table of n, a(n) for n = 1..210</a>
%F A304006 Empirical: a(n) = 5*a(n-1) -6*a(n-2) -9*a(n-4) +8*a(n-5) +36*a(n-6) -29*a(n-7) +34*a(n-8) -88*a(n-9) +8*a(n-10) -70*a(n-11) +205*a(n-12) +66*a(n-13) -377*a(n-14) -29*a(n-15) +420*a(n-16) +897*a(n-17) -1329*a(n-18) -1792*a(n-19) +3267*a(n-20) +1953*a(n-21) -3000*a(n-22) -1986*a(n-23) -1836*a(n-24) +4857*a(n-25) -812*a(n-26) +2460*a(n-27) -5658*a(n-28) -21869*a(n-29) +5879*a(n-30) +37979*a(n-31) +39222*a(n-32) -53345*a(n-33) -60350*a(n-34) +80033*a(n-35) +55646*a(n-36) -80249*a(n-37) -99116*a(n-38) +97246*a(n-39) +113723*a(n-40) -115592*a(n-41) -82690*a(n-42) +63249*a(n-43) +23806*a(n-44) -67251*a(n-45) +52726*a(n-46) +64947*a(n-47) -59223*a(n-48) +4895*a(n-49) +22611*a(n-50) -5950*a(n-51) +1369*a(n-52) +5125*a(n-53) -13309*a(n-54) -19653*a(n-55) +5627*a(n-56) +2405*a(n-57) +1342*a(n-58) +2478*a(n-59) +2088*a(n-60) +435*a(n-61) -1017*a(n-62) -263*a(n-63) -116*a(n-64) +64*a(n-65) -96*a(n-66) +48*a(n-67) for n>70.
%e A304006 Some solutions for n=5
%e A304006 ..0..0..1..1. .0..1..1..1. .0..1..1..0. .0..1..0..0. .0..0..0..0
%e A304006 ..0..0..1..1. .1..0..0..0. .0..1..0..1. .1..0..1..1. .0..0..0..0
%e A304006 ..0..0..1..1. .0..1..1..0. .0..0..1..0. .1..0..1..0. .1..1..1..1
%e A304006 ..0..0..1..1. .0..1..0..1. .0..1..0..0. .0..1..0..0. .1..1..1..1
%e A304006 ..0..0..1..1. .1..0..0..1. .0..1..1..1. .1..0..0..1. .1..1..1..1
%Y A304006 Cf. A304010.
%K A304006 nonn
%O A304006 1,2
%A A304006 _R. H. Hardin_, May 04 2018