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A202691 Triangle read by rows: number of type B snakes according to their last value.

%I A202691 #14 Oct 20 2014 17:15:13
%S A202691 1,0,0,1,1,1,3,3,2,2,1,0,0,3,6,8,8,10,11,11,57,57,54,48,40,40,32,22,
%T A202691 11,0,0,57,114,168,216,256,256,296,328,350,361,361
%N A202691 Triangle read by rows: number of type B snakes according to their last value.
%C A202691 "The table counting snakes of type B by their last value is obtained by the following algorithm: first separate the picture by the column p = 0 and then compute two triangles. Put 1 at the top of the left triangle and 0 at the top of the right one and compute the rest as follows: fill the second row of the left (resp. right) triangle as the sum of the elements of the first row (resp. strictly) to their left. Then fill the third row of the right (resp. left) triangle as the sum of the elements of the previous row (resp. strictly) to their right. Compute all rows successively by reading from left to right and right to left alternately." [Joshuat-Verges et al.]
%H A202691 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, 2011
%e A202691 Triangle begins:
%e A202691                    1 0
%e A202691                  0 1 1 1
%e A202691                3 3 2 2 1 0
%e A202691              0 3 6 8 8 10 11 11
%e A202691       57 57 54 48 40 40 32 22 11 0
%e A202691 0 57 114 168 216 256 256 296 328 350 361 361
%Y A202691 Cf. A185356, A202690, A202704.
%K A202691 nonn,tabf,more
%O A202691 1,7
%A A202691 _N. J. A. Sloane_, Dec 22 2011