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A212194 Triangle T(n,k), n>=1, 0<=k<=n^2, read by rows: row n gives the coefficients of the chromatic polynomial of the staggered hexagonal square grid graph SH_(n,n), highest powers first. 15
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, -3101089710 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

T differs from A212162 first at (n,k) = (5,10): T(5,10) = -3101089710, A212162(5,10) = -3101089711.

The staggered hexagonal square grid graph SH_(n,n) has n^2 = A000290(n) vertices and (n-1)*(3*n-1) = A045944(n-1) edges. The chromatic polynomial of SH_(n,n) has n^2+1 = A002522(n) coefficients.

LINKS

Alois P. Heinz, Rows n = 1..8, flattened

Wikipedia, Chromatic Polynomial

EXAMPLE

3 example graphs:                        o--o--o

.                                        | /|\ |

.                                        |/ | \|

.                            o--o        o--o--o

.                            | /|        | /|\ |

.                            |/ |        |/ | \|

.               o            o--o        o--o--o

Graph:       SH_(1,1)      SH_(2,2)      SH_(3,3)

Vertices:       1             4             9

Edges:          0             5            16

The staggered hexagonal square grid graph SH_(2,2) has chromatic polynomial 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, ... , -3101089710, ...

1,  -85,  3520,  -94620,  1855860,  -28306676, ...

1, -120,  7068, -272344,  7720110, -171656543, ...

1, -161, 12782, -667058, 25738055, -783003395, ...

CROSSREFS

Columns 1-2 give: A000012, (-1)*A045944(n-1).

Row sums (for n>1) and last elements of rows give: A000004, row lengths give: A002522.

Cf. A000290, A212162, A212195.

Sequence in context: A198612 A019907 A248007 * A212162 A249445 A199450

Adjacent sequences:  A212191 A212192 A212193 * A212195 A212196 A212197

KEYWORD

sign,tabf

AUTHOR

Alois P. Heinz, May 03 2012

STATUS

approved

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Last modified January 25 14:14 EST 2022. Contains 350572 sequences. (Running on oeis4.)