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A150179
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, 0), (-1, 1, -1), (0, 1, 1), (1, -1, -1), (1, 0, 1)}.
0
1, 2, 6, 20, 78, 294, 1232, 5054, 21840, 94060, 414734, 1841452, 8258804, 37354536, 169989700, 778394626, 3584284230, 16570124008, 76984172720, 358776753034, 1678242178310, 7874377974572, 37042326513184, 174754402790452, 826160373343962, 3914741263937712, 18587462489170296, 88408330271653002
OFFSET
0,2
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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A027215 A150177 A150178 * A150180 A370947 A150181
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved