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%I #4 Dec 26 2014 12:54:43
%S 341,540,998,1866,3894,8340,18180,40264,89212,198458,445860,999676,
%T 2237366,5016646,11269984,25320924,56833694,127532734,286483406,
%U 643804434,1445740702,3245814338,7290747006,16380214556,36791610106
%N Number of (n+2)X(2+2) 0..3 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order
%C Column 2 of A253044
%H R. H. Hardin, <a href="/A253038/b253038.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +4*a(n-2) +15*a(n-4) -88*a(n-5) -107*a(n-6) +69*a(n-7) +208*a(n-8) +1570*a(n-9) +623*a(n-10) -2575*a(n-11) -6085*a(n-12) -12938*a(n-13) +8665*a(n-14) +33677*a(n-15) +47606*a(n-16) +37948*a(n-17) -135552*a(n-18) -192203*a(n-19) -136886*a(n-20) +93850*a(n-21) +716500*a(n-22) +430864*a(n-23) -588*a(n-24) -841362*a(n-25) -1722932*a(n-26) +53076*a(n-27) +397976*a(n-28) +1827456*a(n-29) +2007160*a(n-30) -1043680*a(n-31) +865480*a(n-32) -2408520*a(n-33) -2494080*a(n-34) -707600*a(n-35) -2686832*a(n-36) +6166048*a(n-37) +4181856*a(n-38) +1880160*a(n-39) -1085312*a(n-40) -10104640*a(n-41) -313024*a(n-42) +1998208*a(n-43) +3442688*a(n-44) +3872256*a(n-45) -4363008*a(n-46) -91648*a(n-47) +326656*a(n-48) +128000*a(n-49) +844800*a(n-50) -2213888*a(n-51) +593920*a(n-52) +1159168*a(n-53) -520192*a(n-54) -16384*a(n-55) -32768*a(n-56) +16384*a(n-57) for n>61
%e Some solutions for n=4
%e ..0..0..1..1....0..0..1..1....0..1..1..2....0..1..1..0....0..1..1..0
%e ..2..0..2..2....1..1..0..0....2..2..1..1....2..2..1..2....0..2..0..2
%e ..0..1..1..2....0..1..0..1....2..1..2..2....2..1..2..2....2..2..0..0
%e ..2..1..1..0....0..2..2..1....3..2..2..1....3..1..1..0....0..0..2..2
%e ..0..2..0..0....2..2..0..2....3..1..3..1....2..2..1..2....2..0..2..0
%e ..2..2..1..1....0..0..2..2....1..1..3..3....2..1..2..2....2..1..1..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 26 2014
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