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Number of nX4 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
1

%I #4 Jan 19 2018 08:35:34

%S 1,16,11,161,478,2459,15248,78163,390424,2230213,11957077,62686390,

%T 343644381,1857612208,9915556165,53695082023,290087274436,

%U 1558866184902,8413068514505,45404547945468,244554296256136,1318757750900979

%N Number of nX4 0..1 arrays with every element equal to 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

%C Column 4 of A298454.

%H R. H. Hardin, <a href="/A298450/b298450.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +9*a(n-2) +89*a(n-3) -204*a(n-4) -742*a(n-5) -2336*a(n-6) +5414*a(n-7) +16164*a(n-8) +22227*a(n-9) -51019*a(n-10) -155268*a(n-11) -9076*a(n-12) +216908*a(n-13) +348123*a(n-14) -565918*a(n-15) -423553*a(n-16) +2275697*a(n-17) +3018514*a(n-18) -4744310*a(n-19) -10714755*a(n-20) +1120597*a(n-21) +12707044*a(n-22) +14767028*a(n-23) -6781707*a(n-24) -13692035*a(n-25) -12330114*a(n-26) -4671661*a(n-27) +21721296*a(n-28) +14985223*a(n-29) +2432193*a(n-30) -25320474*a(n-31) -22704558*a(n-32) +17445078*a(n-33) +34393194*a(n-34) +3452869*a(n-35) -42645667*a(n-36) +551512*a(n-37) +18308956*a(n-38) -481318*a(n-39) -3378385*a(n-40) +2303479*a(n-41) +23871*a(n-42) -1901808*a(n-43) -170904*a(n-44) +588909*a(n-45) +106391*a(n-46) -40247*a(n-47) -13426*a(n-48) -10996*a(n-49) -462*a(n-50) +308*a(n-51) -40*a(n-52) +40*a(n-53) for n>56

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Cf. A298454.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 19 2018