A150832 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), (0, -1, 0), (0, 0, -1), (0, 0, 1), (1, 1, 1)}.

1, 2, 8, 32, 136, 592, 2648, 11990, 55074, 254872, 1189782, 5583716, 26357530, 124899804, 594321530, 2836365206, 13578542630, 65155629342, 313399306562, 1510280824886, 7292109006652, 35262965638096, 170791641548826, 828277652362014, 4022096119160992, 19552674685876310, 95156599107911284

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[i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A150831 A084607 A006139 * A150833 A198760 A150834

Adjacent sequences: A150829 A150830 A150831 * A150833 A150834 A150835

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved