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%I #8 Apr 27 2021 20:57:01
%S 17,129,775,4193,23059,124431,680991,3698901,20206283,110016923,
%T 600355767,3271586963,17843919361,97271016715,530426786593,
%U 2891844158939,15768179521109,85971178631931,468755026926535,2555792909067505
%N Number of n X 3 0..2 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1) X 4 0..2 array without adjacent equal elements in the latter.
%C Column 3 of A229521.
%H R. H. Hardin, <a href="/A229516/b229516.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 25*a(n-2) - 20*a(n-3) - 102*a(n-4) + 151*a(n-5) - 18*a(n-6) + 5*a(n-7) + 231*a(n-8) + 419*a(n-9) - 945*a(n-10) - 472*a(n-11) + 2170*a(n-12) + 574*a(n-13) + 1442*a(n-14) - 3690*a(n-15) + 1136*a(n-16) - 1022*a(n-17) - 1356*a(n-18) + 1988*a(n-19) - 911*a(n-20) - 417*a(n-21) + 603*a(n-22) - 5369*a(n-23) + 8946*a(n-24) - 6852*a(n-25) + 3802*a(n-26) + 1216*a(n-27) - 4313*a(n-28) + 4655*a(n-29) - 3958*a(n-30) + 2476*a(n-31) + 1330*a(n-32) - 2970*a(n-33) + 2524*a(n-34) - 1231*a(n-35) - 456*a(n-36) + 800*a(n-37) - 387*a(n-38) + 142*a(n-39) - 29*a(n-40) - 44*a(n-41) + 36*a(n-42) - 12*a(n-43) + 4*a(n-44) for n > 45.
%e Some solutions for n=3:
%e 0 1 1 1 0 1 1 2 1 1 1 2 1 1 1 2 0 2 1 1 1
%e 2 0 1 1 1 1 2 0 2 1 1 1 1 1 0 0 1 0 1 1 1
%e 0 2 1 2 1 1 1 2 1 0 1 0 2 0 2 1 1 1 0 1 2
%Y Cf. A229521.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 25 2013
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