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A148831
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, 0, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1)}.
0
1, 1, 3, 8, 27, 88, 309, 1081, 3925, 14238, 52786, 195861, 736210, 2772008, 10526439, 40035856, 153181152, 586992985, 2258768052, 8704799117, 33650052792, 130249984973, 505360173122, 1963049571575, 7639344022424, 29760359577584, 116106189246036, 453389564588822, 1772591908018920
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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148828 A148829 A148830 * A029892 A148832 A148833
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved