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A148076 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), (-1, 1, 0), (0, 0, 1), (1, 0, -1)} 0
1, 1, 2, 4, 9, 21, 61, 174, 529, 1641, 5095, 16033, 53457, 179040, 611600, 2114005, 7286191, 25434141, 90624740, 324820786, 1175997883, 4277780903, 15565099278, 57172451188, 211915699815, 789384452140, 2957220530771, 11099880354961, 41758569166532, 158093763382620, 601507196523586, 2297362832884187 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A048194 A148075 A058718 * A217976 A156801 A057580

Adjacent sequences:  A148073 A148074 A148075 * A148077 A148078 A148079

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 24 13:05 EST 2020. Contains 332209 sequences. (Running on oeis4.)