A150155 - OEIS

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A150155

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

1, 2, 6, 20, 74, 291, 1195, 5068, 22018, 97498, 438339, 1995159, 9173968, 42541779, 198690351, 933641950, 4410158539, 20926372152, 99689221688, 476548879546, 2285049484476, 10986607335194, 52952241855106, 255769548269627, 1237835644726379, 6001297807417808, 29142328504083948, 141722186389127649

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + 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: A150153 A150154 A006850 * A150156 A150157 A371712

Adjacent sequences: A150152 A150153 A150154 * A150156 A150157 A150158

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved