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%I #6 Apr 26 2021 21:32:31
%S 236,131328,123551744,123833679872,127365174788096,132364161848967168,
%T 138127371171167993856,144372294092575012290560,
%U 150991906277433156745297920,157951736213079507379343589376
%N Number of n X 6 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
%C Column 6 of A233202.
%H R. H. Hardin, <a href="/A233200/b233200.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2624*a(n-1) -2916352*a(n-2) +2023751680*a(n-3) -1022873305088*a(n-4) +396210733056000*a(n-5) -117075448369774592*a(n-6) +24978582014512857088*a(n-7) -3235719238675389743104*a(n-8) +32228191279027496943616*a(n-9) +79127659192314522138312704*a(n-10) -14330945495506960134011092992*a(n-11) +573127552562903399144703918080*a(n-12) +175763191005253023447780744495104*a(n-13) -41436012082310191504073111849926656*a(n-14) +7185129802334419767282615543889133568*a(n-15) -1237277610717122610430160500786185895936*a(n-16) +170446905899499762382455179339748584980480*a(n-17) -17499361001276181422067502561786112042336256*a(n-18) +1430383734999503249937564429831586312219525120*a(n-19) -95447189449711067045772874206934987245596180480*a(n-20) +4407340875076004112707987073660040981149921574912*a(n-21) -93536104789177786765035829293842113257979682750464*a(n-22) for n > 23.
%e Some solutions for n=2
%e ..0..1..0..1..0..2....0..1..2..6..3..2....0..1..2..7..6..2....0..1..2..1..3..1
%e ..3..2..3..2..6..3....2..0..4..2..0..6....2..0..6..5..3..0....2..4..0..2..7..2
%Y Cf. A233202.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 05 2013
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