A151416 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, 0)}.

1, 1, 2, 5, 13, 37, 109, 334, 1049, 3367, 10992, 36399, 121982, 412969, 1410446, 4854123, 16818222, 58617286, 205384162, 723043647, 2556317905, 9072825097, 32314370528, 115462754160, 413775789826, 1486835229283, 5356049103946, 19338799943334, 69975443521895, 253704568761743, 921550558422286, 3353248008103356

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 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: A005961 A036249 A126031 * A193114 A114509 A003080

Adjacent sequences: A151413 A151414 A151415 * A151417 A151418 A151419

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved