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A241370 T(n,k)=Number of nXk 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

%I A241370 #6 Jul 23 2025 11:14:11
%S A241370 1,1,2,2,7,5,4,28,47,14,8,121,460,326,41,16,523,4617,7376,2284,122,32,
%T A241370 2261,46245,169982,118488,16026,365,64,9775,463567,3910194,6280325,
%U A241370 1904096,112458,1094,128,42261,4646421,90008909,332185927,232173463
%N A241370 T(n,k)=Number of nXk 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.
%C A241370 Table starts
%C A241370 ....1.......1..........2..............4.................8...................16
%C A241370 ....2.......7.........28............121...............523.................2261
%C A241370 ....5......47........460...........4617.............46245...............463567
%C A241370 ...14.....326.......7376.........169982...........3910194.............90008909
%C A241370 ...41....2284.....118488........6280325.........332185927..........17583615124
%C A241370 ..122...16026....1904096......232173463.......28238828935........3437694358689
%C A241370 ..365..112458...30598800.....8582759752.....2400505507498......672068364873884
%C A241370 .1094..789166..491723328...317280724429...204061855414167...131390467341043995
%C A241370 .3281.5537942.7902006144.11729003927933.17346886991310331.25687100469219790719
%H A241370 R. H. Hardin, <a href="/A241370/b241370.txt">Table of n, a(n) for n = 1..144</a>
%F A241370 Empirical for column k:
%F A241370 k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A241370 k=2: a(n) = 7*a(n-1) +2*a(n-3) -8*a(n-4) for n>5
%F A241370 k=3: [order 8]
%F A241370 k=4: [order 31]
%F A241370 k=5: [order 94]
%F A241370 Empirical for row n:
%F A241370 n=1: a(n) = 2*a(n-1) for n>2
%F A241370 n=2: a(n) = 5*a(n-1) -2*a(n-2) -4*a(n-3) for n>5
%F A241370 n=3: a(n) = 9*a(n-1) +16*a(n-2) -50*a(n-3) -72*a(n-4) -32*a(n-5) -32*a(n-6) for n>8
%F A241370 n=4: [order 21] for n>23
%F A241370 n=5: [order 65] for n>67
%e A241370 Some solutions for n=4 k=4
%e A241370 ..0..1..0..1....0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2
%e A241370 ..1..1..2..0....1..0..2..1....0..2..0..0....2..0..0..1....0..1..2..1
%e A241370 ..1..2..2..0....2..0..0..1....1..2..0..0....1..0..2..0....2..0..1..0
%e A241370 ..1..2..2..1....0..1..0..2....0..1..0..1....2..0..1..2....1..0..1..0
%Y A241370 Column 1 is A007051(n-1)
%Y A241370 Row 1 is A000079(n-2)
%K A241370 nonn,tabl
%O A241370 1,3
%A A241370 _R. H. Hardin_, Apr 20 2014