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T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,1,1,1 for x=0,1,2,3,4
7

%I #5 Mar 31 2012 12:36:30

%S 1,1,1,2,5,2,3,14,14,3,4,43,67,43,4,6,124,338,338,124,6,9,352,1646,

%T 3021,1646,352,9,13,1025,8085,25962,25962,8085,1025,13,19,2977,39748,

%U 221082,384758,221082,39748,2977,19,28,8619,194964,1924263,5833286,5833286

%N T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,1,1,1 for x=0,1,2,3,4

%C Every 0 is next to 0 3's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's

%C Table starts

%C ..1.....1.......2..........3............4..............6.................9

%C ..1.....5......14.........43..........124............352..............1025

%C ..2....14......67........338.........1646...........8085.............39748

%C ..3....43.....338.......3021........25962.........221082...........1924263

%C ..4...124....1646......25962.......384758........5833286..........88309448

%C ..6...352....8085.....221082......5833286......153517349........4052348046

%C ..9..1025...39748....1924263.....88309448.....4052348046......186804530634

%C .13..2977..194964...16672219...1329981026...106662154198.....8622121723045

%C .19..8619..957860..144064579..20064521716..2816548576990...397804283640646

%C .28.24982.4707712.1245052112.303052845328.74313847621002.18336405515418246

%H R. H. Hardin, <a href="/A197782/b197782.txt">Table of n, a(n) for n = 1..144</a>

%e Some solutions containing all values 0 to 4 for n=6 k=4

%e ..1..2..2..1....2..1..1..2....0..0..1..2....1..3..1..2....1..2..0..0

%e ..0..1..1..0....1..1..0..1....0..0..0..1....2..1..4..1....0..1..1..2

%e ..2..1..3..1....0..2..2..1....1..2..0..0....2..1..1..3....2..1..4..1

%e ..1..1..2..2....0..1..1..0....3..1..0..0....1..0..2..1....1..0..1..3

%e ..1..4..1..1....2..1..4..1....1..4..1..2....0..0..0..1....1..0..2..1

%e ..2..1..0..0....1..3..1..2....2..1..3..1....0..0..1..2....2..1..0..0

%Y Column 1 is A000930

%Y Column 2 is A197607

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Oct 18 2011