Andrew Howroyd, <a href="/A208054/b208054_1.txt">Table of n, a(n) for n = 1..231</a> (terms 1..49 from R. H. Hardin)

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T(n,k) = Number of nXk n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).

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T(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).

Equivalently, the number of colorings in the rhombic hexagonal square grid graph RH_(n,nk) using any number of colors up to permutation of the colors. - _Andrew Howroyd_, Jun 25 2017

R. H. Hardin, Andrew Howroyd, <a href="/A208054/b208054_1.txt">Table of n, a(n) for n = 1..231</a> (terms 1..49</a> from R. H. Hardin)

Cf. A207868, A212162, A212163, A208050, A068271.

R. H. Hardin , Feb 22 2012

Table starts

...1.........1.............2................5................15

...1.........2............15..............203..............4140

...2........15...........716............83440..........18171918

...5.......203.........83440........112073062......346212384169

..15......4140......18171918.....346212384169.18633407199331522

..52....115975....6423127757.2043836452962923

.203...4213597.3376465219485

.877.190899322

Equivalently, the number of colorings in the rhombic hexagonal square grid graph RH_(n,n) using any number of colors up to permutation of the colors.

Table starts

...1.........1.............2................5................15

...1.........2............15..............203..............4140

...2........15...........716............83440..........18171918

...5.......203.........83440........112073062......346212384169

..15......4140......18171918.....346212384169.18633407199331522

..52....115975....6423127757.2043836452962923

.203...4213597.3376465219485

.877.190899322

...

Column Columns 1 is -5 are A000110(n-1), A020557(n-1), A208051, A208052, A208053.

Column 2 is A020557(n-1)

Cf. A212162, A212163, A208050, A068271.

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_R. H. Hardin (rhhardin(AT)att.net) _ Feb 22 2012

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approved

R. H. Hardin, <a href="/A208054/b208054.txt">Table of n, a(n) for n = 1..49</a>

allocated for Ron HardinT(n,k)=Number of nXk nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

1, 1, 1, 2, 2, 2, 5, 15, 15, 5, 15, 203, 716, 203, 15, 52, 4140, 83440, 83440, 4140, 52, 203, 115975, 18171918, 112073062, 18171918, 115975, 203, 877, 4213597, 6423127757, 346212384169, 346212384169, 6423127757, 4213597, 877, 4140, 190899322

1,4

Table starts

...1.........1.............2................5................15

...1.........2............15..............203..............4140

...2........15...........716............83440..........18171918

...5.......203.........83440........112073062......346212384169

..15......4140......18171918.....346212384169.18633407199331522

..52....115975....6423127757.2043836452962923

.203...4213597.3376465219485

.877.190899322

Some solutions for n=4 k=3

..0..1..0....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0

..2..3..1....2..3..4....2..3..2....2..3..1....2..3..0....2..3..1....2..3..2

..4..2..4....0..5..0....0..4..0....0..4..5....4..5..3....4..5..3....0..1..4

..0..5..0....1..2..1....1..2..1....5..3..4....0..1..0....0..6..4....2..0..1

Column 1 is A000110(n-1)

Column 2 is A020557(n-1)

allocated

nonn,tabl

R. H. Hardin (rhhardin(AT)att.net) Feb 22 2012

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