A150433 - OEIS

A150433

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

1, 2, 7, 24, 98, 409, 1758, 7795, 35205, 160821, 742982, 3468265, 16299943, 77032454, 366093124, 1747822983, 8373252262, 40244756832, 194020661020, 937661379787, 4541152148976, 22038088224223, 107142362306562, 521689401171770, 2543796653210565, 12420216127882598, 60712953181549129, 297092174378811714

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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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150431 A302185 A150432 * A197554 A325581 A162044

Adjacent sequences: A150430 A150431 A150432 * A150434 A150435 A150436

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved