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A202692 The first of three triangles counting 3-colored alternating permutations by their last value.

%I A202692 #18 Oct 20 2021 12:38:49
%S A202692 1,0,1,9,9,8,0,9,18,26,405,405,396,378,352,0,405,810,1206,1584,1936,
%T A202692 44469,44469,44064,43254,42048,40464,38528,0,44469,88938,133002,
%U A202692 176256,218304,258768,297296,9086985,9086985,9042516,8953578,8820576,8644320,8426016,8167248,7869952
%N A202692 The first of three triangles counting 3-colored alternating permutations by their last value.
%C A202692 "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.]
%H A202692 Georg Fischer and Sean. A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a202/A202692.java">Java program source code</a>
%H A202692 M. Josuat-Verges, J.-C. Novelli and J.-Y. Thibon, <a href="http://arxiv.org/abs/1110.5272">The algebraic combinatorics of snakes</a>, arXiv preprint arXiv:1110.5272 [math.CO], 2011.
%e A202692 The triangle begins:
%e A202692 1
%e A202692 0 1
%e A202692 9 9 8
%e A202692 0 9 18 26
%e A202692 405 405 396 378 352
%e A202692 ...
%e A202692 The three triangles together:
%e A202692 1                     1                      1
%e A202692 0 1                   1 2                    2 3
%e A202692 9 9 8                 8 7 5                  5 3 0
%e A202692 0 9 18 26             26 34 41 46            46 51 54 54
%e A202692 405 405 396 378 352   352 326 292 251 205    205 159 108 54 0
%o A202692 (Java) /* Cf. link */
%Y A202692 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.
%K A202692 nonn,tabl
%O A202692 1,4
%A A202692 _N. J. A. Sloane_, Dec 23 2011
%E A202692 More terms from _Georg Fischer_, Oct 20 2021