A150193 - OEIS

A150193

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

1, 2, 6, 21, 78, 308, 1265, 5348, 23112, 101665, 453631, 2047531, 9331915, 42881889, 198431612, 923766634, 4323106334, 20325027924, 95946992266, 454570567870, 2160603679333, 10299336123028, 49224393332004, 235820966155703, 1132198038582156, 5446512972682182, 26248173239453764, 126706988418088708

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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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A150192 A287211 A357538 * A052300 A306832 A121941

Adjacent sequences: A150190 A150191 A150192 * A150194 A150195 A150196

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved