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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. 20
 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 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: A035377 A136274 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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