A148839 - OEIS

A148839

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

1, 1, 3, 8, 27, 90, 319, 1133, 4205, 15759, 60427, 233074, 913214, 3602736, 14365891, 57610031, 232900379, 946343007, 3869179663, 15888284571, 65568408186, 271629504874, 1129897836137, 4715762928864, 19749860841934, 82957158492855, 349484850458876, 1476158463333397, 6251072188077864

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OFFSET

0,3

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, 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] + aux[1 + i, 1 + 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: A148836 A148837 A148838 * A148840 A374570 A047153

Adjacent sequences: A148836 A148837 A148838 * A148840 A148841 A148842

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved