A149903 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, 1, 0), (0, 1, 1), (1, -1, -1)}.

1, 2, 5, 14, 47, 163, 587, 2197, 8502, 33375, 133304, 542650, 2233956, 9279163, 38962506, 165122173, 703984127, 3020900731, 13051779861, 56676234344, 247160539208, 1083014298642, 4765947405530, 21042946045519, 93222182853153, 414404313407641, 1847436708413576, 8256834170357613

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[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, 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: A149902 A047026 A148338 * A149904 A287888 A115276

Adjacent sequences: A149900 A149901 A149902 * A149904 A149905 A149906

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved