A151495 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, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)}

1, 1, 6, 22, 112, 556, 2992, 16416, 93040, 537004, 3156300, 18805948, 113415860, 690920348, 4246311084, 26297470908, 163962253192, 1028405157316, 6484807032820, 41086983729464, 261446728122772, 1670163037965324, 10707288651740680, 68867225024134936, 444264596237129308, 2873850125874850068

Offset

0,3

Links

Table of n, a(n) for n=0..25.

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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A100300 A027296 A179601 * A193463 A319214 A009358

Adjacent sequences: A151492 A151493 A151494 * A151496 A151497 A151498

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved