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A233217 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

%I A233217 #6 Jul 23 2025 07:56:09
%S A233217 1,2,3,6,23,11,23,376,452,48,99,7222,35446,10313,236,452,147019,
%T A233217 3054973,3638416,249062,1248,2136,3054973,268289572,1340889772,
%U A233217 380283286,6147803,6896,10313,63927526,23644611625,496475792293,591021089923,39892988056
%N A233217 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
%C A233217 Table starts
%C A233217 ....1.........2.............6.................23.....................99
%C A233217 ....3........23...........376...............7222.................147019
%C A233217 ...11.......452.........35446............3054973..............268289572
%C A233217 ...48.....10313.......3638416.........1340889772...........496475792293
%C A233217 ..236....249062.....380283286.......591021089923........919538740854193
%C A233217 .1248...6147803...39892988056....260625046992322....1703198747507336644
%C A233217 .6896.152986472.4187991850726.114934898294104873.3154729081272072714436
%H A233217 R. H. Hardin, <a href="/A233217/b233217.txt">Table of n, a(n) for n = 1..161</a>
%F A233217 Empirical for column k:
%F A233217 k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
%F A233217 k=2: a(n) = 35*a(n-1) -259*a(n-2) +225*a(n-3)
%F A233217 k=3: a(n) = 127*a(n-1) -2331*a(n-2) +2205*a(n-3)
%F A233217 k=4: a(n) = 491*a(n-1) -22099*a(n-2) +21609*a(n-3)
%F A233217 k=5: a(n) = 1975*a(n-1) -228357*a(n-2) +1804281*a(n-3) -4170978*a(n-4) +2593080*a(n-5)
%F A233217 k=6: [order 7]
%F A233217 k=7: [order 11]
%F A233217 Empirical for row n:
%F A233217 n=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
%F A233217 n=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3) for n>4
%F A233217 n=3: a(n) = 111*a(n-1) -2128*a(n-2) +10532*a(n-3) -17559*a(n-4) +9045*a(n-5) for n>7
%F A233217 n=4: [order 9] for n>12
%F A233217 n=5: [order 19] for n>23
%F A233217 n=6: [order 42] for n>47
%e A233217 Some solutions for n=3 k=4
%e A233217 ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1
%e A233217 ..2..1..2..1....0..1..5..1....0..2..2..1....2..0..0..0....0..2..1..3
%e A233217 ..2..0..2..2....1..5..1..0....4..0..1..0....0..1..3..5....2..0..0..2
%Y A233217 Column 1 is A233162(n+1)
%Y A233217 Row 1 is A233106
%K A233217 nonn,tabl
%O A233217 1,2
%A A233217 _R. H. Hardin_, Dec 06 2013