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A151306
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), (1, 0), (1, 1)}
0
1, 2, 9, 29, 139, 511, 2498, 9781, 48238, 196055, 971491, 4047652, 20113296, 85304735, 424646194, 1825369912, 9097470592, 39520352083, 197127302029, 863661309954, 4310448703844, 19018425833689, 94959280164706, 421465934703502, 2105044748278047, 9390456216012559, 46912406079449786, 210193393267663019
OFFSET
0,2
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, 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: A268568 A150902 A150903 * A150904 A122675 A042357
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved