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A148097 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, 0, 1), (0, 1, -1), (1, -1, 0)} 0
1, 1, 2, 4, 10, 26, 72, 210, 633, 1965, 6255, 20320, 67115, 225180, 765236, 2629300, 9128886, 31973878, 112868208, 401357573, 1436347656, 5170091107, 18710588629, 68041269378, 248527107385, 911543126026, 3355925436811, 12398020132566, 45952857513263, 170833589869361, 636858717536370, 2380437498466650 (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, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A154835 A049145 A102407 * A148098 A210043 A049130

Adjacent sequences:  A148094 A148095 A148096 * A148098 A148099 A148100

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)