%I #4 Dec 24 2014 17:10:13
%S 754,8151,90512,1012633,11398109,128428125,1448958659,16350990527,
%T 184573462153,2083620529861,23523516898805,265578356196015,
%U 2998415143533036,33852657688469658,382204657874593618
%N Number of (1+2)X(n+2) 0..3 arrays with every consecutive three elements in every row having 2 or 3 distinct values, in every column 1 or 2 distinct values, in every diagonal 2 distinct values, and in every antidiagonal 2 distinct values, and new values 0 upwards introduced in row major order
%C Row 1 of A252917
%H R. H. Hardin, <a href="/A252918/b252918.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 15*a(n-1) +10*a(n-2) -765*a(n-3) +1171*a(n-4) +12116*a(n-5) -20692*a(n-6) -95780*a(n-7) +85294*a(n-8) +518328*a(n-9) +370181*a(n-10) -1717459*a(n-11) -5062996*a(n-12) -574947*a(n-13) +21720107*a(n-14) +29475588*a(n-15) -34296234*a(n-16) -94875324*a(n-17) -41567880*a(n-18) +27210088*a(n-19) +204910683*a(n-20) +511458105*a(n-21) -40779726*a(n-22) -1298126295*a(n-23) -1283621717*a(n-24) +1465124634*a(n-25) +3268887464*a(n-26) -588474630*a(n-27) -3691574274*a(n-28) -1492053424*a(n-29) +2285036572*a(n-30) +3123218360*a(n-31) -803144868*a(n-32) -3009081352*a(n-33) +68388696*a(n-34) +1603528992*a(n-35) +173836104*a(n-36) -264956112*a(n-37) -9840528*a(n-38) +11632032*a(n-39) -684288*a(n-40) for n>41
%e Some solutions for n=2
%e ..0..0..1..0....0..1..0..2....0..1..2..1....0..0..1..2....0..1..2..3
%e ..2..0..3..3....0..3..3..1....1..1..2..2....0..1..0..3....0..2..3..2
%e ..0..3..1..3....0..3..0..1....1..2..0..1....3..0..0..2....1..2..2..3
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 24 2014