A151417 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 1), (0, 1), (1, -1), (1, 1)}.

1, 1, 2, 5, 14, 40, 122, 380, 1217, 3967, 13137, 44053, 149321, 510735, 1760687, 6111171, 21338857, 74906438, 264192659, 935757437, 3327107090, 11870683108, 42486960839, 152506832992, 548875377127, 1980241926132, 7160483990345, 25946243999559, 94199923539220, 342620238726110, 1248274347651947

Offset

0,3

Links

Table of n, a(n) for n=0..30.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A148320 A301871 A076866 * A045632 A148321 A007463

Adjacent sequences: A151414 A151415 A151416 * A151418 A151419 A151420

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved