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A151356
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), (1, -1), (1, 1)}.
0
1, 0, 1, 2, 8, 22, 101, 364, 1618, 6702, 30512, 135904, 634610, 2958340, 14147829, 67996988, 331941976, 1631261090, 8101797506, 40502662220, 204075069854, 1034325813080, 5274800747204, 27039112223056, 139308940725640, 720950926411856, 3747030865713930, 19550315832999732, 102379532471138668
OFFSET
0,4
LINKS
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 46, Tag. Tag 53.
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, 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: A053958 A300370 A191643 * A238530 A303287 A321068
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved