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A151260 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, 0), (0, 1), (1, -1)}. 0
1, 1, 2, 5, 15, 40, 129, 410, 1357, 4554, 15889, 55393, 198101, 714134, 2608715, 9604663, 35746763, 133855284, 505329127, 1918867073, 7331462511, 28154364640, 108675692369, 421316437364, 1640430104775, 6411619948398, 25151938110261, 98999303611753, 390913037555343, 1548142631022968, 6148391182189065 (list; graph; refs; listen; history; text; internal format)
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[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[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
CROSSREFS
Sequence in context: A148346 A148347 A309299 * A148348 A148349 A076865
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified February 26 12:54 EST 2024. Contains 370352 sequences. (Running on oeis4.)