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A151293
Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, 1), (1, -1), (1, 1)}.
0
1, 2, 7, 24, 88, 328, 1246, 4779, 18485, 71918, 281102, 1102653, 4337842, 17104951, 67577658, 267410057, 1059581561, 4203221319, 16689714274, 66324649355, 263761185264, 1049579758069, 4178825351781, 16645543692333, 66331807758634, 264426232745902, 1054454512710944, 4206064951123326
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, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
CROSSREFS
Sequence in context: A270490 A104625 A221454 * A122446 A150390 A052705
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved