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A151289
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, 1)}
0
1, 2, 7, 21, 80, 267, 1042, 3655, 14400, 51960, 205770, 756169, 3003754, 11179972, 44496878, 167181919, 666257284, 2521360818, 10057256094, 38278262216, 152783755958, 584199222356, 2332875408218, 8954456162165, 35770374449310, 137743370071244, 550391555936678, 2125263063052980
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, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
CROSSREFS
Sequence in context: A319852 A060900 A305850 * A150300 A150301 A150302
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved