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A206238 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.

%I A206238 #7 Jul 22 2025 19:20:39
%S A206238 15,60,60,310,256,310,1640,1136,1136,1640,8910,5728,4456,5728,8910,
%T A206238 51066,31652,27168,27168,31652,51066,294546,170728,133392,283728,
%U A206238 133392,170728,294546,1710184,943584,607008,1236432,1236432,607008,943584,1710184
%N A206238 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly two equal edges, and new values 0..3 introduced in row major order.
%C A206238 Table starts
%C A206238 ......15......60......310......1640........8910........51066........294546
%C A206238 ......60.....256.....1136......5728.......31652.......170728........943584
%C A206238 .....310....1136.....4456.....27168......133392.......607008.......3503136
%C A206238 ....1640....5728....27168....283728.....1236432......9042600......95322432
%C A206238 ....8910...31652...133392...1236432....10915392....118573968....1122086640
%C A206238 ...51066..170728...607008...9042600...118573968...1448239080...22535636736
%C A206238 ..294546..943584..3503136..95322432..1122086640..22535636736..649065145152
%C A206238 .1710184.5175034.17206032.419146392.10022726928.303011941944.8026428934128
%H A206238 R. H. Hardin, <a href="/A206238/b206238.txt">Table of n, a(n) for n = 1..544</a>
%F A206238 Empirical for column k:
%F A206238 k=1: a(n) = 8*a(n-1) -11*a(n-2) +36*a(n-3) -303*a(n-4) +232*a(n-5) +147*a(n-6) +756*a(n-7) for n>8
%F A206238 k=2: a(n) = 3*a(n-1) +20*a(n-2) -14*a(n-3) -133*a(n-4) +95*a(n-5) +123*a(n-6) +9*a(n-7) -102*a(n-8) for n>10
%F A206238 k=3: a(n) = a(n-1) +129*a(n-3) -129*a(n-4) for n>7
%F A206238 k=4: a(n) = a(n-1) +339*a(n-3) -339*a(n-4) for n>8
%F A206238 k=5: a(n) = a(n-1) +921*a(n-3) -921*a(n-4) for n>9
%F A206238 k=6: a(n) = a(n-1) +2571*a(n-3) -2571*a(n-4) for n>10
%F A206238 k=7: a(n) = a(n-1) +7329*a(n-3) -7329*a(n-4) for n>11
%F A206238 k=8: a(n) = a(n-1) +21219*a(n-3) -21219*a(n-4) for n>12
%F A206238 k=9: a(n) = a(n-1) +62121*a(n-3) -62121*a(n-4) for n>13
%F A206238 k=10: a(n) = a(n-1) +183291*a(n-3) -183291*a(n-4) for n>14
%F A206238 k=11: a(n) = a(n-1) +543729*a(n-3) -543729*a(n-4) for n>15
%F A206238 apparently a(n) = a(n-1) +3*A085279(k+1)*a(n-3) -3*A085279(k+1)*a(n-4) for k>2 and n>k+4
%e A206238 Some solutions for n=4 k=3
%e A206238 ..0..0..1..0....0..0..1..1....0..0..1..1....0..1..2..0....0..0..1..1
%e A206238 ..0..1..0..0....0..2..3..3....2..2..3..1....3..2..2..0....2..2..0..1
%e A206238 ..2..0..0..1....2..3..3..2....1..2..2..3....2..2..1..2....3..2..2..3
%e A206238 ..0..0..2..3....3..3..0..3....0..1..2..2....2..1..2..2....2..1..2..2
%e A206238 ..0..1..3..3....0..0..3..3....0..0..3..2....3..2..2..3....2..2..0..2
%K A206238 nonn,tabl
%O A206238 1,1
%A A206238 _R. H. Hardin_ Feb 05 2012