A151470 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), (-1, 0), (-1, 1), (0, 1), (1, 0), (1, 1)}.

1, 1, 6, 18, 94, 386, 1979, 9262, 47785, 238604, 1246969, 6454615, 34187874, 180940665, 969918088, 5211150923, 28218545331, 153283951381, 837083867878, 4585637886067, 25219366928380, 139092895929290, 769504571196682, 4267822299499544, 23729769950773771, 132230104921510603, 738390549104421575

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 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: A104970 A216727 A174075 * A280096 A009573 A052655

Adjacent sequences: A151467 A151468 A151469 * A151471 A151472 A151473

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved