A150194 - OEIS

A150194

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

1, 2, 6, 21, 79, 303, 1215, 4987, 20714, 87388, 373220, 1606108, 6966239, 30432499, 133645431, 589776713, 2614755682, 11636407959, 51961981179, 232786535938, 1045829291187, 4710551425147, 21268096578127, 96235878784582, 436327558629890, 1982000429167932, 9018867256480052, 41105488663112547

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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[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A052300 A306832 A121941 * A150195 A363810 A150196

Adjacent sequences: A150191 A150192 A150193 * A150195 A150196 A150197

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved