A151432 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), (0, 1), (1, 0), (1, 1)}.

1, 1, 4, 12, 45, 174, 693, 2891, 12156, 52538, 228973, 1012996, 4518961, 20342820, 92221108, 420719274, 1930067929, 8897118329, 41194214136, 191470957420, 893110958485, 4179139628301, 19612391986898, 92283693683299, 435288156265051, 2057796624112995, 9748277239594671, 46268733559268079

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 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: A149368 A200539 A149369 * A188312 A006735 A166115

Adjacent sequences: A151429 A151430 A151431 * A151433 A151434 A151435

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved