A148659 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, 0, 1), (-1, 1, -1), (1, -1, -1), (1, 1, 0)}

1, 1, 3, 6, 25, 65, 263, 818, 3480, 11449, 50576, 175792, 786179, 2849879, 12909894, 48120645, 220751593, 841416548, 3890986045, 15126720815, 70373188247, 277921541613, 1300723463955, 5202857448347, 24471964794706, 99008148878483, 467470249736998, 1910257010864032, 9050595168800827

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A174473 A148657 A148658 * A148660 A148661 A148662

Adjacent sequences: A148656 A148657 A148658 * A148660 A148661 A148662

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved