A150965 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, 1), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 167, 732, 3564, 16437, 80742, 381990, 1886365, 9058918, 44881863, 217608631, 1080496305, 5273126110, 26223071353, 128577465870, 640125864687, 3149641710093, 15693652174663, 77424611596144, 386027793424796, 1908453086549949, 9519983895827832, 47143699831058313, 235260137129936359

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A150962 A150963 A150964 * A150966 A185034 A185234

Adjacent sequences: A150962 A150963 A150964 * A150966 A150967 A150968

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved