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A229315 Number of nX2 0..3 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1)X3 0..3 array without adjacent equal elements in the latter.

%I A229315 #6 Jul 23 2025 05:40:06
%S A229315 14,154,1494,13968,129766,1203222,11146054,103236194,956057048,
%T A229315 8853833056,81991894696,759294338246,7031507356914,65115840648102,
%U A229315 603010344430850,5584224380804470,51713144710842856,478893600594242612
%N A229315 Number of nX2 0..3 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1)X3 0..3 array without adjacent equal elements in the latter.
%C A229315 Column 2 of A229320
%H A229315 R. H. Hardin, <a href="/A229315/b229315.txt">Table of n, a(n) for n = 1..176</a>
%F A229315 Empirical: a(n) = 12*a(n-1) -12*a(n-2) -170*a(n-3) +413*a(n-4) +360*a(n-5) -2500*a(n-6) +4761*a(n-7) -7424*a(n-8) +8095*a(n-9) +1067*a(n-10) -10948*a(n-11) +5811*a(n-12) -5685*a(n-13) -5667*a(n-14) +43767*a(n-15) -42200*a(n-16) +63250*a(n-17) -114786*a(n-18) +139663*a(n-19) -210040*a(n-20) +242074*a(n-21) +11485*a(n-22) -229841*a(n-23) +246874*a(n-24) -495364*a(n-25) +424756*a(n-26) -414970*a(n-27) +601244*a(n-28) -811641*a(n-29) +1009456*a(n-30) -1380235*a(n-31) +1228145*a(n-32) -674904*a(n-33) +313339*a(n-34) +511282*a(n-35) -710123*a(n-36) +664496*a(n-37) -457843*a(n-38) +191690*a(n-39) +55758*a(n-40) -66502*a(n-41) +150610*a(n-42) +1481*a(n-43) +19304*a(n-44) -48928*a(n-45) +40006*a(n-46) -47878*a(n-47) -42105*a(n-48) -11482*a(n-49) -12568*a(n-50) +16105*a(n-51) +103*a(n-52) +5809*a(n-53) -2122*a(n-54) +4423*a(n-55) +601*a(n-56) -1525*a(n-57) -384*a(n-58) -1331*a(n-59) -98*a(n-60) +157*a(n-61) +5*a(n-62) +86*a(n-63) +11*a(n-64) -2*a(n-65)
%e A229315 Some solutions for n=3
%e A229315 ..1..3....2..3....3..1....2..3....2..1....0..3....2..0....1..1....1..2....1..1
%e A229315 ..3..1....1..0....2..2....2..0....3..1....2..2....0..2....0..2....2..3....0..2
%e A229315 ..1..1....0..1....3..1....0..3....1..0....1..0....2..0....1..1....3..0....3..2
%K A229315 nonn
%O A229315 1,1
%A A229315 _R. H. Hardin_ Sep 19 2013