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Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
1

%I #4 Jan 29 2017 12:38:20

%S 5,110,609,2808,12191,49986,201450,795220,3098932,11944444,45648773,

%T 173194466,653072024,2449607050,9146028282,34010834368,126024445869,

%U 465494253234,1714507604630,6298717534388,23086454425976,84439440608072

%N Number of nX5 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Column 5 of A281765.

%H R. H. Hardin, <a href="/A281762/b281762.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) -29*a(n-2) +2*a(n-3) +52*a(n-4) +170*a(n-5) -239*a(n-6) -674*a(n-7) +73*a(n-8) +1874*a(n-9) +1456*a(n-10) -3556*a(n-11) -2269*a(n-12) +228*a(n-13) +7955*a(n-14) -1394*a(n-15) -5270*a(n-16) -4208*a(n-17) -6664*a(n-18) +6626*a(n-19) +10430*a(n-20) +21576*a(n-21) -48939*a(n-22) +56684*a(n-23) -32865*a(n-24) +17584*a(n-25) +71780*a(n-26) -98666*a(n-27) +76825*a(n-28) -82636*a(n-29) -20094*a(n-30) -4536*a(n-31) -85926*a(n-32) -352*a(n-33) -69440*a(n-34) -14036*a(n-35) -30493*a(n-36) -20432*a(n-37) -9763*a(n-38) -14256*a(n-39) -787*a(n-40) -5248*a(n-41) -1167*a(n-42) -738*a(n-43) -218*a(n-44) +76*a(n-45) -209*a(n-46) +120*a(n-47) -16*a(n-48) for n>57

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281765.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 29 2017