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A148473 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, 0), (-1, 0, 1), (0, -1, 0), (0, 0, 1), (1, 1, -1)} 0
1, 1, 2, 6, 20, 65, 226, 838, 3201, 12386, 48948, 197608, 809096, 3345155, 13980334, 59041103, 251334992, 1076995274, 4645807488, 20164588874, 87973297367, 385580488738, 1697545399851, 7504250584691, 33293669209338, 148208341418642, 661867001127396, 2964446051683526, 13313133410772356 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A181301 A302612 A005726 * A000718 A148474 A156831

Adjacent sequences:  A148470 A148471 A148472 * A148474 A148475 A148476

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)