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A212208
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Triangle T(n,k), n>=1, 0<=k<=n^2, read by rows: row n gives the coefficients of the chromatic polynomial of the square diagonal grid graph DG_(n,n), highest powers first.
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19
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1, 0, 1, -6, 11, -6, 0, 1, -20, 174, -859, 2627, -5082, 6048, -4023, 1134, 0, 1, -42, 825, -10054, 85011, -528254, 2491825, -9084089, 25795983, -57031153, 97292827, -125639547, 118705077, -77301243, 30931875, -5709042, 0, 1, -72, 2492, -55183, 877812
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OFFSET
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1,4
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COMMENTS
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The square diagonal grid graph DG_(n,n) has n^2 = A000290(n) vertices and 2*(n-1)*(2*n-1) = A002943(n-1) edges. The chromatic polynomial of DG_(n,n) has n^2+1 = A002522(n) coefficients.
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LINKS
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EXAMPLE
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3 example graphs: o---o---o
. |\ /|\ /|
. | X | X |
. |/ \|/ \|
. o---o o---o---o
. |\ /| |\ /|\ /|
. | X | | X | X |
. |/ \| |/ \|/ \|
. o o---o o---o---o
Graph: DG_(1,1) DG_(2,2) DG_(3,3)
Vertices: 1 4 9
Edges: 0 6 20
The square diagonal grid graph DG_(2,2) equals the complete graph K_4 and has chromatic polynomial q*(q-1)*(q-2)*(q-3) = q^4 -6*q^3 +11*q^2 -6*q => row 2 = [1, -6, 11, -6, 0].
Triangle T(n,k) begins:
1, 0;
1, -6, 11, -6, 0;
1, -20, 174, -859, 2627, -5082, ...
1, -42, 825, -10054, 85011, -528254, ...
1, -72, 2492, -55183, 877812, -10676360, ...
1, -110, 5895, -205054, 5203946, -102687204, ...
1, -156, 11946, -598491, 22059705, -637802510, ...
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CROSSREFS
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Row sums (for n>1) and last elements of rows give: A000004, row lengths give: A002522.
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KEYWORD
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sign,tabf
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AUTHOR
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STATUS
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approved
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