A149326 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, 0, 0), (-1, 0, 1), (0, -1, 0), (0, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 38, 143, 527, 1977, 7851, 31110, 125198, 515302, 2125456, 8872634, 37425969, 158422833, 676318450, 2903753155, 12514755832, 54252313270, 236067482292, 1030845976142, 4519733509516, 19873168554659, 87648421496810, 387702292340412, 1719006136669141, 7640989054526988

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A354341 A149324 A149325 * A149327 A308446 A334458

Adjacent sequences: A149323 A149324 A149325 * A149327 A149328 A149329

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved