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A223300 4X4X4 triangular graph coloring a rectangular array: number of nX3 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223300 #6 Jul 23 2025 03:58:19
%S A223300 144,3132,76788,1882500,46589268,1148040516,28402185108,700525554180,
%T A223300 17321067229140,427424478219972,10564355081565972,260773436696057988,
%U A223300 6443737539288281940,159091220790299549508,3930517719610405689492
%N A223300 4X4X4 triangular graph coloring a rectangular array: number of nX3 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223300 Column 3 of A223305
%H A223300 R. H. Hardin, <a href="/A223300/b223300.txt">Table of n, a(n) for n = 1..210</a>
%F A223300 Empirical: a(n) = 10*a(n-1) +500*a(n-2) -2878*a(n-3) -15863*a(n-4) +79004*a(n-5) +144196*a(n-6) -616760*a(n-7) -363504*a(n-8) +1348864*a(n-9) +396544*a(n-10) -600576*a(n-11) for n>12
%e A223300 Some solutions for n=3
%e A223300 ..2..1..4....7..4..1....7..4..2....1..2..1....9..8..5....9..8..4....5..4..3
%e A223300 ..4..3..7....4..1..4....6..3..1....2..1..0....5..9..8....8..4..8....4..3..4
%e A223300 ..7..4..3....1..4..8....7..4..2....1..2..1....9..5..9....9..8..7....8..4..7
%K A223300 nonn
%O A223300 1,1
%A A223300 _R. H. Hardin_ Mar 19 2013