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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..13, 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: A253669 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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