A151151 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), (0, 1, 1), (1, 0, 0), (1, 1, 1)}

1, 3, 11, 47, 205, 927, 4273, 19921, 93761, 444517, 2118833, 10146089, 48764565, 235101077, 1136445415, 5505870237, 26727374589, 129968044895, 632964986425, 3086839690155, 15072285466445, 73675540585185, 360497744553655, 1765544372027673, 8654028910135843, 42451454274028333, 208389423187010269

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, k, -1 + n] + aux[i, -1 + 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: A151148 A151149 A151150 * A151152 A151153 A151154

Adjacent sequences: A151148 A151149 A151150 * A151152 A151153 A151154

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved