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A151267
Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (1, -1), (1, 1)}
0
1, 1, 3, 7, 21, 55, 165, 457, 1371, 3909, 11727, 33993, 101979, 298629, 895887, 2640931, 7922793, 23460851, 70382553, 209078319, 627234957, 1867531435, 5602594305, 16709292259, 50127876777, 149690954499, 449072863497, 1342297451651, 4026892354953, 12045410486339, 36136231459017, 108154061971965
OFFSET
0,3
LINKS
M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
CROSSREFS
Sequence in context: A192068 A368098 A318395 * A319558 A307251 A320803
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved