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A233113 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

%I A233113 #6 Jul 23 2025 07:53:43
%S A233113 1,2,2,6,19,6,23,313,313,23,99,6046,24912,6046,99,452,123352,2154065,
%T A233113 2154065,123352,452,2136,2565169,189286871,794723482,189286871,
%U A233113 2565169,2136,10313,53692063,16683923848,294285758398,294285758398,16683923848
%N A233113 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
%C A233113 Table starts
%C A233113 ....1........2.............6................23.....................99
%C A233113 ....2.......19...........313..............6046.................123352
%C A233113 ....6......313.........24912...........2154065..............189286871
%C A233113 ...23.....6046.......2154065.........794723482...........294285758398
%C A233113 ...99...123352.....189286871......294285758398........457873555330159
%C A233113 ..452..2565169...16683923848...109015274761891.....712427482567592092
%C A233113 .2136.53692063.1471365099497.40385221182281560.1108502928092713640626
%H A233113 R. H. Hardin, <a href="/A233113/b233113.txt">Table of n, a(n) for n = 1..180</a>
%F A233113 Empirical for column k:
%F A233113 k=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
%F A233113 k=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3)
%F A233113 k=3: a(n) = 111*a(n-1) -2128*a(n-2) +10532*a(n-3) -17559*a(n-4) +9045*a(n-5)
%F A233113 k=4: [order 7]
%F A233113 k=5: [order 15]
%e A233113 Some solutions for n=3 k=4
%e A233113 ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..0
%e A233113 ..0..2..2..5....1..1..0..2....1..0..4..2....2..4..2..5....0..0..1..0
%e A233113 ..0..2..1..2....2..1..1..5....0..1..3..1....4..0..0..3....2..2..0..1
%K A233113 nonn,tabl
%O A233113 1,2
%A A233113 _R. H. Hardin_, Dec 04 2013