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A148811
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, 0, 0), (0, 1, 1), (1, -1, -1), (1, 1, -1)}.
0
1, 1, 3, 8, 26, 86, 309, 1108, 4177, 16043, 62131, 245624, 988058, 3974672, 16249872, 67146327, 277391652, 1159193515, 4883667639, 20554100144, 87291612458, 373042330747, 1592243882405, 6845720258023, 29580989452406, 127649661170533, 554181473820419, 2415949131968238, 10517688992163295
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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A148809 A151457 A148810 * A148812 A148813 A369618
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved