A151363 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, 0), (-1, 1), (0, -1), (0, 1), (1, 0)}.

1, 0, 2, 1, 10, 14, 75, 178, 738, 2304, 8753, 31186, 117244, 444107, 1698959, 6637212, 25978768, 103470800, 413378548, 1671251159, 6788681873, 27799009080, 114434701571, 473862635406, 1972068523477, 8246133103745, 34634859230481, 146059305983882, 618344086849853, 2627035342133955

Offset

0,3

Links

Table of n, a(n) for n=0..29.

A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 23.

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[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[aux[0, 0, n], {n, 0, 25}]

Crossrefs

Sequence in context: A290596 A151504 A151507 * A213303 A213304 A196130

Adjacent sequences: A151360 A151361 A151362 * A151364 A151365 A151366

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved