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A148667
Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, 0, 0), (0, -1, 1), (1, 1, 0)}
0
1, 1, 3, 7, 19, 60, 169, 539, 1713, 5412, 18241, 58932, 197794, 670464, 2252141, 7793403, 26523661, 91645156, 319356023, 1106651892, 3895231214, 13604856592, 47889319173, 169562551244, 598458138702, 2132024158112, 7562668836374, 26957742010368, 96480822451924, 344633309569472, 1238725757557789
OFFSET
0,3
LINKS
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
MATHEMATICA
aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
CROSSREFS
Sequence in context: A268125 A287484 A201169 * A148668 A148669 A249380
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved