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A223301 4X4X4 triangular graph coloring a rectangular array: number of nX4 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 A223301 #6 Jul 23 2025 03:58:26
%S A223301 576,30564,1882500,118001928,7442199324,470062209228,29706324866280,
%T A223301 1877636655597516,118686588470619204,7502399551962981216,
%U A223301 474244299620974794852,29978170786284871362588,1894997177822538169880160
%N A223301 4X4X4 triangular graph coloring a rectangular array: number of nX4 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 A223301 Column 4 of A223305
%H A223301 R. H. Hardin, <a href="/A223301/b223301.txt">Table of n, a(n) for n = 1..210</a>
%F A223301 Empirical: a(n) = 94*a(n-1) -1666*a(n-2) -33696*a(n-3) +1100794*a(n-4) -4373330*a(n-5) -96641317*a(n-6) +770139565*a(n-7) +2078815868*a(n-8) -30815999776*a(n-9) +9439379121*a(n-10) +508827706118*a(n-11) -740346550259*a(n-12) -3820163432470*a(n-13) +8313303065134*a(n-14) +11790417886127*a(n-15) -37600871363022*a(n-16) -5093748767428*a(n-17) +69398396589688*a(n-18) -28648799032000*a(n-19) -44260499027840*a(n-20) +28257350216960*a(n-21) +9517866926336*a(n-22) -7538371685376*a(n-23) -621543923712*a(n-24) +546106392576*a(n-25) for n>26
%e A223301 Some solutions for n=3
%e A223301 ..1..4..3..7....0..2..5..9....0..1..4..8....1..3..1..4....5..2..5..2
%e A223301 ..0..1..4..8....2..5..4..8....2..4..2..5....0..1..4..8....2..1..4..1
%e A223301 ..1..3..7..4....5..4..8..9....4..7..4..2....2..4..8..7....4..3..1..4
%K A223301 nonn
%O A223301 1,1
%A A223301 _R. H. Hardin_ Mar 19 2013