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A212162
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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 rhombic hexagonal square grid graph RH_(n,n), highest powers first.
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21
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1, 0, 1, -5, 8, -4, 0, 1, -16, 112, -448, 1120, -1791, 1786, -1012, 248, 0, 1, -33, 510, -4898, 32703, -160859, 602408, -1749715, 3975561, -7068408, 9755858, -10265148, 7968348, -4304712, 1445104, -226720, 0, 1, -56, 1508, -25992, 321994, -3051871, 23000726, -141421592, 722137763, -3101089711
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OFFSET
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1,4
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COMMENTS
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T differs from A212194 first at (n,k) = (5,10): T(5,10) = -3101089711, A212194(5,10) = -3101089710.
The rhombic hexagonal square grid graph RH_(n,n) has n^2 = A000290(n) vertices and (n-1)*(3*n-1) = A045944(n-1) edges. The chromatic polynomial of RH_(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
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. o--o o--o--o
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. o o--o o--o--o
Graph: RH_(1,1) RH_(2,2) RH_(3,3)
Vertices: 1 4 9
Edges: 0 5 16
The rhombic hexagonal square grid graph RH_(2,2) has chromatic polynomial q*(q-1)*(q-2)^2 = q^4 -5*q^3 +8*q^2 -4*q => row 2 = [1, -5, 8, -4, 0].
Triangle T(n,k) begins:
1, 0;
1, -5, 8, -4, 0;
1, -16, 112, -448, 1120, -1791, ...
1, -33, 510, -4898, 32703, -160859, ...
1, -56, 1508, -25992, 321994, -3051871, ... , -3101089711, ...
1, -85, 3520, -94620, 1855860, -28306676, ...
1, -120, 7068, -272344, 7720110, -171656543, ...
1, -161, 12782, -667058, 25738055, -783003395, ...
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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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