A151339 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, -1), (-1, 1), (0, 1), (1, 0)}.

1, 0, 0, 2, 2, 0, 16, 44, 28, 192, 934, 1402, 3476, 20246, 50790, 99972, 469618, 1624064, 3609582, 12454800, 49484974, 133986816, 389029068, 1515899106, 4833068324, 13708903398, 48687650964, 170176839110, 509652229334, 1672521448054, 5973355611550, 19172414057922, 61007425374108, 213401708600242

Offset

0,4

Links

Table of n, a(n) for n=0..33.

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 4, Tag 18.

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

Crossrefs

Sequence in context: A369072 A091466 A134085 * A228273 A069521 A245687

Adjacent sequences: A151336 A151337 A151338 * A151340 A151341 A151342

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved