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A202692
The first of three triangles counting 3-colored alternating permutations by their last value.
12
1, 0, 1, 9, 9, 8, 0, 9, 18, 26, 405, 405, 396, 378, 352, 0, 405, 810, 1206, 1584, 1936, 44469, 44469, 44064, 43254, 42048, 40464, 38528, 0, 44469, 88938, 133002, 176256, 218304, 258768, 297296, 9086985, 9086985, 9042516, 8953578, 8820576, 8644320, 8426016, 8167248, 7869952
OFFSET
1,4
COMMENTS
"The table counting alternating permutations with r colors by their last value is obtained by the following algorithm: first separate the picture by the column p = 0 and then compute r triangles. Put 1 at the top of each triangle and compute the rest as follows: fill the second row of all triangles as the sum of the elements of the first row strictly to their left. Then fill the third row of all triangles as the sum of the elements of the previous row to their right. Compute all rows successively by reading from left to right and right to left alternately." [Joshuat-Verges et al.]
LINKS
Georg Fischer and Sean. A. Irvine, Java program source code
M. Josuat-Verges, J.-C. Novelli and J.-Y. Thibon, The algebraic combinatorics of snakes, arXiv preprint arXiv:1110.5272 [math.CO], 2011.
EXAMPLE
The triangle begins:
1
0 1
9 9 8
0 9 18 26
405 405 396 378 352
...
The three triangles together:
1 1 1
0 1 1 2 2 3
9 9 8 8 7 5 5 3 0
0 9 18 26 26 34 41 46 46 51 54 54
405 405 396 378 352 352 326 292 251 205 205 159 108 54 0
PROG
(Java) /* Cf. link */
CROSSREFS
The three triangles with initial 1,1,1 are A202692, A202693, A202694; with 1,0,0: A202695, A202696, A202697; with 0,1,0: A202698, A202699, A202700; with 0,0,1: A202701, A202702, A202703.
Sequence in context: A344688 A346451 A347059 * A259149 A292825 A347058
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Dec 23 2011
EXTENSIONS
More terms from Georg Fischer, Oct 20 2021
STATUS
approved