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A150033 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), (0, 0, 1), (0, 1, -1), (1, 0, 1)}. 0
1, 2, 6, 17, 56, 187, 647, 2283, 8183, 29742, 109129, 403667, 1504455, 5637671, 21235076, 80333014, 305030726, 1162135296, 4440424269, 17010967118, 65320831670, 251350805303, 969033651846, 3742365310049, 14475611770191, 56073194209612, 217494453475571, 844640587355439, 3283870660839249 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A108630 A338735 A161408 * A150034 A238127 A190915

Adjacent sequences:  A150030 A150031 A150032 * A150034 A150035 A150036

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 28 21:30 EST 2021. Contains 349415 sequences. (Running on oeis4.)