A149575 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, 1, -1), (1, 1, 1)}

1, 1, 5, 13, 65, 209, 1045, 3729, 18645, 70717, 353585, 1395805, 6979025, 28339645, 141698225, 587614085, 2938070425, 12383615985, 61918079925, 264376635889, 1321883179445, 5704016489345, 28520082446725, 124149831843401, 620749159217005, 2722238024497961, 13611190122489805, 60069831193045649

Offset

0,3

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[-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] + 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: A309167 A272069 A018678 * A156101 A372799 A093118

Adjacent sequences: A149572 A149573 A149574 * A149576 A149577 A149578

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved