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

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, 11, 0, 0, 57, 114, 168, 216, 256, 256, 296, 328, 350, 361, 361

Offset: 1

Author

N. J. A. Sloane, Dec 22 2011

Keywords

• nonn
• tabf
• more

Comments

"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.]

Examples

			Triangle begins:
                   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 11 0
0 57 114 168 216 256 256 296 328 350 361 361
		

Links

• M. Josuat-Verges, J.-C. Novelli and J.-Y. Thibon, The algebraic combinatorics of snakes, arXiv preprint arXiv:1110.5272, 2011

Crossrefs

Cf. A185356, A202690, A202704.