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A148645 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), (-1, 1, 1), (1, 0, 0), (1, 1, -1)}. 0
1, 1, 3, 6, 23, 61, 259, 779, 3436, 11116, 50120, 170775, 782661, 2770992, 12847938, 46827027, 218941164, 816506936, 3842355699, 14601045443, 69068143075, 266598722383, 1266449907569, 4953581862226, 23613990259234, 93420951221186, 446661239295308, 1784662398793558, 8554415627075763 (list; graph; refs; listen; history; text; internal format)
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, j, k, -1 + n] + aux[1 + 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: A148643 A240646 A148644 * A148646 A148647 A148648
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified July 22 06:32 EDT 2024. Contains 374481 sequences. (Running on oeis4.)