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A223350 3X3X3 triangular graph without horizontal edges coloring a rectangular array: number of nX6 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223350 #6 Jul 23 2025 04:02:11
%S A223350 300,22388,1851020,154482340,12912752876,1079538816324,90254934876620,
%T A223350 7545802995190884,630870570544801836,52744249735952687492,
%U A223350 4409709467224003774348,368675973859970441084836
%N A223350 3X3X3 triangular graph without horizontal edges coloring a rectangular array: number of nX6 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223350 Column 6 of A223352
%H A223350 R. H. Hardin, <a href="/A223350/b223350.txt">Table of n, a(n) for n = 1..210</a>
%F A223350 Empirical: a(n) = 105*a(n-1) -1690*a(n-2) -12608*a(n-3) +372616*a(n-4) -412320*a(n-5) -25492864*a(n-6) +95198976*a(n-7) +669344256*a(n-8) -3814535168*a(n-9) -4806082560*a(n-10) +56384290816*a(n-11) -49291067392*a(n-12) -244915896320*a(n-13) +525445627904*a(n-14) -268301238272*a(n-15) -40399536128*a(n-16) +53687091200*a(n-17) -8589934592*a(n-18)
%e A223350 Some solutions for n=3
%e A223350 ..3..1..0..2..4..2....0..1..0..2..4..1....0..1..0..2..0..1....3..1..0..1..4..1
%e A223350 ..1..0..1..4..2..4....2..0..1..0..2..0....1..4..1..4..1..4....1..4..1..3..1..3
%e A223350 ..3..1..3..1..0..2....0..2..4..2..5..2....0..1..4..2..4..1....0..1..0..1..3..1
%K A223350 nonn
%O A223350 1,1
%A A223350 _R. H. Hardin_ Mar 19 2013