A148422 - OEIS

A148422

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

1, 1, 2, 5, 18, 58, 202, 736, 2842, 10959, 43399, 175792, 720009, 2977404, 12486416, 52878780, 225071867, 965947847, 4178003062, 18156229431, 79240920764, 347851189938, 1533662577816, 6782824169642, 30108927878118, 134161530176648, 599433003836445, 2685040503728087, 12061956696161418

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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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A148419 A148420 A148421 * A148423 A148424 A148425

Adjacent sequences: A148419 A148420 A148421 * A148423 A148424 A148425

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved