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A193283 Triangle T(n,k), n>=1, 0<=k<=n*(n+1)/2, read by rows: row n gives the coefficients of the chromatic polynomial of the Triangle Graph of order n, highest powers first. 4
1, 0, 1, -3, 2, 0, 1, -9, 32, -56, 48, -16, 0, 1, -18, 144, -672, 2016, -4031, 5368, -4584, 2272, -496, 0, 1, -30, 419, -3612, 21477, -93207, 304555, -761340, 1463473, -2152758, 2385118, -1929184, 1075936, -369824, 58976, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The Triangle Graph of order n has n rows with i vertices in row i. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The Graph has A000217(n) vertices and 3*A000217(n-1) edges altogether.

LINKS

Alois P. Heinz, Rows n = 1..11, flattened

Eric Weisstein's World of Mathematics, Triangle Graph

Eric Weisstein's World of Mathematics, Chromatic Polynomial

Wikipedia, Chromatic Polynomial

EXAMPLE

4 example graphs:                         o

.                                        / \

.                           o           o---o

.                          / \         / \ / \

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

.                / \     / \ / \     / \ / \ / \

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

Order:      1     2         3             4

Vertices:   1     3         6            10

Edges:      0     3         9            18

The Triangle graph of order 2 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,   0;

1,  -3,   2,      0;

1,  -9,  32,    -56,     48,     -16,       0;

1, -18, 144,   -672,   2016,   -4031,    5368, ...

1, -30, 419,  -3612,  21477,  -93207,  304555, ...

1, -45, 965, -13115, 126720, -925528, 5303300, ...

CROSSREFS

Cf. A000217, A045943, A178435, A182797, A185442, A193233, A193277.

Sequence in context: A054654 A154477 A142071 * A193277 A118972 A171224

Adjacent sequences:  A193280 A193281 A193282 * A193284 A193285 A193286

KEYWORD

sign,hard,look,tabf

AUTHOR

Alois P. Heinz, Jul 20 2011

STATUS

approved

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Last modified December 19 21:19 EST 2014. Contains 252239 sequences.