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%I #10 Feb 14 2024 18:58:28
%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,3,7,7,3,1,1,5,13,25,13,5,1,1,9,16,27,
%T 27,16,9,1,1,17,32,91,106,91,32,17,1,1,31,65,231,316,316,231,65,31,1,
%U 1,57,125,455,835,708,835,455,125,57,1,1,105,211,1135,2350,3572,3572,2350
%N T(n,k) = Number of n X k 0..4 arrays with each element equal to the number of its horizontal and vertical neighbors within one of itself.
%H R. H. Hardin, <a href="/A196017/b196017.txt">Table of n, a(n) for n = 1..312</a>
%e Table starts:
%e .1..1...1....1.....1......1.......1........1.........1..........1...........1
%e .1..1...1....1.....3......5.......9.......17........31.........57.........105
%e .1..1...2....7....13.....16......32.......65.......125........211.........390
%e .1..1...7...25....27.....91.....231......455......1135.......2693........6041
%e .1..3..13...27...106....316.....835.....2350......7232......21846.......63985
%e .1..5..16...91...316....708....3572....14607.....54710.....196832......782926
%e .1..9..32..231...835...3572...22711...100094....517009....2740712....14291156
%e .1.17..65..455..2350..14607..100094...670449...4760391...32900243...226381615
%e .1.31.125.1135..7232..54710..517009..4760391..44864449..411748723..3838635775
%e .1.57.211.2693.21846.196832.2740712.32900243.411748723.5122273171.64922269000
%e Some solutions for n=6 and k=4:
%e ..2..2..2..0....2..2..3..2....2..3..3..2....2..2..3..2....0..2..2..2
%e ..2..0..3..2....2..0..3..3....3..4..3..3....2..0..3..3....2..3..0..2
%e ..3..3..3..3....3..3..3..3....3..3..0..2....3..3..4..3....3..4..3..3
%e ..3..2..0..2....3..2..0..2....3..4..3..3....3..4..4..3....3..3..4..3
%e ..2..0..2..2....2..0..2..2....3..4..4..3....3..4..4..3....2..0..3..3
%e ..2..2..2..0....2..2..2..0....2..3..3..2....2..3..3..2....2..2..3..2
%Y The n-th term of the column 2 is A000213(n-2).
%K nonn,tabl
%O 1,13
%A _R. H. Hardin_, Sep 26 2011