A150830 - OEIS

A150830

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), (0, 1, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 32, 134, 590, 2650, 12064, 55662, 259600, 1218869, 5758394, 27355651, 130518455, 624952568, 3002191966, 14463270457, 69845523330, 338018136262, 1639028367438, 7961255179893, 38729392325035, 188671413533460, 920291819644948, 4494126591423276, 21969562075344127, 107502725460944998

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, 1 + k, -1 + n] + aux[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: A150829 A155084 A322251 * A150831 A084607 A006139

Adjacent sequences: A150827 A150828 A150829 * A150831 A150832 A150833

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved