A202704 -id:A202704 - cp's OEIS frontend

A202819 The right-hand half-triangle of A202704.

1, 0, 1, 1, 1, 0, 3, 4, 5, 5, 17, 14, 10, 5, 0, 105, 122, 136, 146, 151, 151, 811, 706, 584, 448, 302, 151, 0

Offset: 1

N. J. A. Sloane, Dec 25 2011

			Triangle begins:
    1;
    0,   1;
    1,   1,   0;
    3,   4,   5,   5;
   17,  14,  10,   5,   0;
  105, 122, 136, 146, 151, 151;
  811, 706, 584, 448, 302, 151,   0;

Cf. A202704, A202820.

a(22)-a(28) from F. Chapoton, May 24 2022

A202820 The left-hand half-triangle of A202704.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 3, 2, 1, 0, 17, 20, 22, 23, 23, 105, 88, 68, 46, 23, 0

Offset: 1

N. J. A. Sloane, Dec 25 2011

			Triangle begins:
0
0 0
1 1 1
3 2 1 0
17 20 22 23 23
105 88 68 46 23 0

Cf. A202704, A202819.

A202690 The triangle in A185356 with the central column of zeros omitted.

Original entry on oeis.org

1, 1, 0, 1, 1, 2, 4, 4, 3, 3, 2, 0, 0, 4, 8, 11, 11, 14, 16, 16, 80, 80, 76, 68, 57, 57, 46, 32, 16, 0, 0, 80, 160, 236, 304, 361, 361, 418, 464, 496, 512, 512, 3904, 3904, 3824, 3664, 3428, 3124, 2763, 2763, 2402, 1984, 1520, 1024, 512, 0

Offset: 1

N. J. A. Sloane, Dec 22 2011

			Triangle begins:
                     1 1
                 0   1 1   2
             4   4   3 3   2   0
         0   4   8  11 11  14  16  16
    80  80  76  68  57 57  46  32  16  0
  0 80 160 236 304 361 361 418 464 496 512 512

M. Josuat-Vergès, J.-C. Novelli and J.-Y. Thibon, The algebraic combinatorics of snakes, arXiv preprint arXiv:1110.5272 [math.CO], 2011.

Cf. A185356, A202691, A202704.

T(n,k) = {if ((k==0), return(0)); if (n==1, if (abs(k)==1, return(1))); if (n%2, if (k<0, sum(j=k+1, n-1, T(n-1,j)), sum(j=k, n-1, T(n-1,j))), if (k<0, sum(j=-n+1, k, T(n-1,j)), sum(j=-n+1, k-1, T(n-1,j))));}
tabf(nn) = {for (n=1, nn, for (k=-n, n, if (k, print1(T(n, k), ", "));); print;);} \\ Michel Marcus, Jun 03 2020

More terms from Michel Marcus, Jun 03 2020

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

Original entry on oeis.org

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

N. J. A. Sloane, Dec 22 2011

"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.]

			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

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

Cf. A185356, A202690, A202704.

cp's OEIS Frontend

A202819 The right-hand half-triangle of A202704.

Views

Author

Keywords

Examples

Crossrefs

Extensions

A202820 The left-hand half-triangle of A202704.

Views

Author

Keywords

Examples

Crossrefs

A202690 The triangle in A185356 with the central column of zeros omitted.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs