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A198523 Number of nX3 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

%I A198523 #7 Jul 22 2025 12:59:12
%S A198523 5,193,16714,1877316,222590953,26670041125,3201911378187,
%T A198523 384557171168810,46189600128813487,5547962760669962158,
%U A198523 666383179391895903794,80041410904141273707361,9614030302463648373863365
%N A198523 Number of nX3 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.
%C A198523 Column 3 of A198528
%H A198523 R. H. Hardin, <a href="/A198523/b198523.txt">Table of n, a(n) for n = 1..200</a>
%F A198523 Empirical: a(n) = 140*a(n-1) -2296*a(n-2) -11502*a(n-3) +41183*a(n-4) +408760*a(n-5) +595837*a(n-6) -3718654*a(n-7) -13795951*a(n-8) -11064332*a(n-9) +29075688*a(n-10) +108107068*a(n-11) +134930012*a(n-12) -37607560*a(n-13) -266631136*a(n-14) -319325600*a(n-15) -322970496*a(n-16) -229207424*a(n-17) +130810368*a(n-18) +389159424*a(n-19) +272935936*a(n-20) +65761280*a(n-21) -8192000*a(n-22) -6356992*a(n-23) -786432*a(n-24) for n>25
%e A198523 Some solutions for n=4
%e A198523 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1
%e A198523 ..1..2..1....1..2..0....0..1..2....1..2..3....0..1..2....1..2..1....0..0..2
%e A198523 ..3..0..0....3..2..4....2..1..3....4..0..2....2..0..2....3..0..3....3..1..1
%e A198523 ..1..4..0....3..0..3....2..3..0....0..2..3....2..1..3....1..4..0....2..1..1
%K A198523 nonn
%O A198523 1,1
%A A198523 _R. H. Hardin_ Oct 26 2011