A193277 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 gasket graph S_n, highest powers first.
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
Offset: 1
Examples
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, ...
Links
- Alois P. Heinz, Rows n = 1..7, flattened
- Eric Weisstein's World of Mathematics, Chromatic Polynomial.
- Eric Weisstein's World of Mathematics, Sierpiński Gasket Graph.
- Wikipedia, Chromatic Polynomial.
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