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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 k X k X k triangular grid.
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
OFFSET
1,3
COMMENTS
The k X k X k triangular grid 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.
The coefficients of the chromatic polynomials for the column sequences are given by the rows of A193283. - Georg Fischer, Jul 31 2023
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
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.
Sequence in context: A136274 A290976 A114699 * A212163 A212195 A228926
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Dec 02 2010
STATUS
approved