A149390 - OEIS

A149390

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

1, 1, 4, 12, 50, 180, 765, 3057, 13305, 56407, 250672, 1098659, 4964911, 22229939, 101785502, 462852168, 2141109671, 9852233226, 45947914834, 213392971356, 1001817343552, 4687319002195, 22126854983613, 104160214414763, 493973279622712, 2337219155644307, 11127776966787465, 52878820029287643

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OFFSET

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 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: A152123 A149388 A149389 * A149391 A149392 A149393

Adjacent sequences: A149387 A149388 A149389 * A149391 A149392 A149393

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved