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A193277
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Triangle T(n,k), n>=1, 0<=k<=(3+3^n)/2, read by rows: row n gives the coefficients of the chromatic polynomial of the Sierpinski graph S_n, highest powers first.
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4
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1, -3, 2, 0, 1, -9, 32, -56, 48, -16, 0, 1, -27, 339, -2625, 14016, -54647, 160663, -362460, 631828, -848736, 866640, -653248, 343744, -112896, 17408, 0, 1, -81, 3204, -82476, 1553454, -22823259, 272286183, -2711405961, 22990179324
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OFFSET
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1,2
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COMMENTS
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The Sierpinski graph S_n has (3+3^n)/2 vertices and 3^n edges. The chromatic polynomial of S_n has (3+3^n)/2+1 coefficients.
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LINKS
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EXAMPLE
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3 example graphs: o
. / \
. o---o
. / \ / \
. o o---o---o
. / \ / \ / \
. o o---o o---o o---o
. / \ / \ / \ / \ / \ / \ / \
. o---o o---o---o o---o---o---o---o
Graph: S_1 S_2 S_3
Vertices: 3 6 15
Edges: 3 9 27
The Sierpinski graph S_1 is equal to the cycle graph C_3 with chromatic polynomial q^3 -3*q^2 +2*q => [1, -3, 2, 0].
Triangle T(n,k) begins:
1, -3, 2, 0;
1, -9, 32, -56, 48, -16, ...
1, -27, 339, -2625, 14016, -54647, ...
1, -81, 3204, -82476, 1553454, -22823259, ...
1, -243, 29295, -2336013, 138604878, -6526886841, ...
1, -729, 265032, -64069056, 11585834028, -1671710903793, ...
1, -2187, 2389419, -1738877625, 948268049436, -413339609377179, ...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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