A150928 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, 0), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 33, 151, 632, 2968, 13118, 62548, 284927, 1370647, 6366362, 30799646, 144981633, 704284837, 3347236781, 16311676879, 78083501777, 381477237431, 1836320274479, 8989802928902, 43466387142329, 213155231408571, 1034331505114336, 5079587717402180, 24721740035854884, 121558447451358658

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150925 A150926 A150927 * A150929 A150930 A150931

Adjacent sequences: A150925 A150926 A150927 * A150929 A150930 A150931

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved