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A182797 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the Triangle Graph of order k. 22
1, 0, 2, 0, 0, 3, 0, 0, 6, 4, 0, 0, 6, 24, 5, 0, 0, 6, 192, 60, 6, 0, 0, 6, 2112, 1620, 120, 7, 0, 0, 6, 32640, 98820, 7680, 210, 8, 0, 0, 6, 718080, 13638780, 1574400, 26250, 336, 9, 0, 0, 6, 22665216, 4260983940, 1034019840, 13676250, 72576, 504, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The Triangle Graph of order k has k 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(k) vertices and 3*A000217(k-1) edges altogether.

LINKS

Table of n, a(n) for n=1..55.

Eric Weisstein's World of Mathematics, Triangle Graph

Wikipedia, Chromatic polynomial

EXAMPLE

Square array A(n,k) begins:

  1,   0,    0,       0,          0,             0,  ...

  2,   0,    0,       0,          0,             0,  ...

  3,   6,    6,       6,          6,             6,  ...

  4,  24,  192,    2112,      32640,        718080,  ...

  5,  60, 1620,   98820,   13638780,    4260983940,  ...

  6, 120, 7680, 1574400, 1034019840, 2175789895680,  ...

CROSSREFS

Columns k=1-11 give: A000027, A007531, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796.

Rows n=1-10 give: A000007(k-1), A000038(k-1), A040006(k-1), A182798, A153467*4, A153468*5, A153469*6, A153470*7, A153471*8, A153472*9, A153473*10.

Cf. A000217, A193283.

Sequence in context: A136274 A290976 A114699 * A212163 A212195 A228926

Adjacent sequences:  A182794 A182795 A182796 * A182798 A182799 A182800

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Dec 02 2010

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)