A151457 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), (0, 1), (1, -1), (1, 0), (1, 1)}.

1, 1, 3, 8, 26, 86, 302, 1091, 4040, 15271, 58626, 228160, 897769, 3566851, 14287540, 57643690, 234033415, 955486006, 3920368468, 16157046284, 66855815475, 277647691670, 1156870017745, 4834889174037, 20262414041885, 85133911519652, 358538436730899, 1513264706135320, 6399889659608629

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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

Crossrefs

Sequence in context: A148807 A148808 A148809 * A148810 A148811 A148812

Adjacent sequences: A151454 A151455 A151456 * A151458 A151459 A151460

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved