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A233173 Number of nX7 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

%I A233173 #6 Jun 02 2025 08:51:38
%S A233173 528,1009664,2385772544,5896922988544,14822434649669632,
%T A233173 37512454919740719104,95229762257179140685824,
%U A233173 242105801211204186752942080,615953046875285234718796152832
%N A233173 Number of nX7 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
%C A233173 Column 7 of A233174
%H A233173 R. H. Hardin, <a href="/A233173/b233173.txt">Table of n, a(n) for n = 1..210</a>
%F A233173 Empirical: a(n) = 5376*a(n-1) -9666560*a(n-2) +6641680384*a(n-3) -514859204608*a(n-4) -1288661987491840*a(n-5) +418421348973412352*a(n-6) +37913553463018520576*a(n-7) -32422674725335864442880*a(n-8) +2456986406781633163165696*a(n-9) +743294581445578569579233280*a(n-10) -127145448531964683219491618816*a(n-11) -541734166879150708735933939712*a(n-12) +1458065585310949453860586897014784*a(n-13) -105361096550619343762748861090627584*a(n-14) +324477988839219423442308126073683968*a(n-15) +230584711190673160155410811484335243264*a(n-16) -7433042952429249561278089081087686868992*a(n-17) -29094142371740238626118528935416182079488*a(n-18) +4137833581758611715714635226370301451304960*a(n-19) -44601490397061246283071436545296723011960832*a(n-20)
%e A233173 Some solutions for n=2
%e A233173 ..0..1..0..1..0..2..5....0..1..0..1..0..2..0....0..1..0..1..5..2..4
%e A233173 ..3..1..2..1..5..2..4....5..4..3..4..5..4..5....5..4..5..2..0..2..1
%K A233173 nonn
%O A233173 1,1
%A A233173 _R. H. Hardin_, Dec 05 2013