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

1,7

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.]

Links

Table of n, a(n) for n=1..42.

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

Example

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

Crossrefs

Cf. A185356, A202690, A202704.

Sequence in context: A338113 A309119 A308725 * A328143 A278402 A276415

Adjacent sequences: A202688 A202689 A202690 * A202692 A202693 A202694

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Dec 22 2011

Status

approved