A151349 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, 0), (-1, 1), (0, -1), (0, 1), (1, -1)}.

1, 0, 1, 1, 5, 8, 40, 91, 406, 1167, 4956, 16349, 68312, 246502, 1027322, 3938800, 16499271, 65979431, 278832735, 1149369374, 4907324239, 20691994829, 89274013063, 383084876832, 1669457571727, 7264787659538, 31956494188222, 140668018518295, 624084995417305, 2773778482274832

Offset

0,5

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 45, Tag 48

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

Crossrefs

Sequence in context: A176859 A176757 A280965 * A298935 A258786 A192272

Adjacent sequences: A151346 A151347 A151348 * A151350 A151351 A151352

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved