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A214105 Number of 0..2 colorings of a 6X(n+1) array circular in the n+1 direction with new values 0..2 introduced in row major order.

%I A214105 #6 Jul 22 2025 23:07:32
%S A214105 243,32,31307,38880,6214031,19920544,1400634371,7553900384,
%T A214105 333634652748,2494628888576,82026663625611,764829357599840,
%U A214105 20608425761163112,224394973731792512,5262099379377937907,64035391192104272352
%N A214105 Number of 0..2 colorings of a 6X(n+1) array circular in the n+1 direction with new values 0..2 introduced in row major order.
%C A214105 Row 6 of A214101
%H A214105 R. H. Hardin, <a href="/A214105/b214105.txt">Table of n, a(n) for n = 1..210</a>
%F A214105 Empirical: a(n) = 31*a(n-1) +13*a(n-2) -9267*a(n-3) +78227*a(n-4) +638291*a(n-5) -10708528*a(n-6) +6150128*a(n-7) +536501107*a(n-8) -2033164909*a(n-9) -11904211731*a(n-10) +84436380845*a(n-11) +77412169368*a(n-12) -1706545467464*a(n-13) +1811776247266*a(n-14) +19304523636130*a(n-15) -47889544867794*a(n-16) -117456145818834*a(n-17) +525235170302850*a(n-18) +213625076617474*a(n-19) -3290233046207679*a(n-20) +2089968288107233*a(n-21) +12240390785511137*a(n-22) -17809441292578591*a(n-23) -24715178090410237*a(n-24) +65443537376780099*a(n-25) +13041358597027717*a(n-26) -135368827365208891*a(n-27) +55864333777538925*a(n-28) +159221485635535469*a(n-29) -143613070053648912*a(n-30) -91023260463361328*a(n-31) +154989094709985664*a(n-32) +916845169402240*a(n-33) -84356499484710528*a(n-34) +27208165877275008*a(n-35) +20331945994935040*a(n-36) -12539801202332928*a(n-37) -634009016424448*a(n-38) +1714850626521088*a(n-39) -304729578209280*a(n-40)
%e A214105 Some solutions for n=4
%e A214105 ..0..1..0..2..1....0..1..2..0..1....0..1..0..2..1....0..1..2..1..2
%e A214105 ..2..0..2..1..0....1..0..1..2..0....2..0..2..1..0....1..2..0..2..0
%e A214105 ..1..2..1..0..2....0..1..0..1..2....0..1..0..2..1....2..0..2..0..1
%e A214105 ..2..0..2..1..0....1..0..1..2..0....2..0..2..1..0....1..2..1..2..0
%e A214105 ..0..1..0..2..1....0..2..0..1..2....0..2..0..2..1....0..1..2..1..2
%e A214105 ..1..2..1..0..2....2..1..2..0..1....1..0..1..0..2....1..2..1..2..0
%K A214105 nonn
%O A214105 1,1
%A A214105 _R. H. Hardin_ Jul 04 2012