A151251 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), (0, 0, 1), (0, 1, 0), (1, 1, 0), (1, 1, 1)}.

1, 4, 18, 84, 400, 1928, 9368, 45776, 224608, 1105536, 5454784, 26966272, 133518464, 661936512, 3285120384, 16318182656, 81118238208, 403499984896, 2008203312128, 9999508994048, 49811499909120, 248220669087744, 1237327213948928, 6169546670055424, 30770185224601600, 153498159158099968

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + 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: A014348 A126020 A086405 * A293490 A010849 A007859

Adjacent sequences: A151248 A151249 A151250 * A151252 A151253 A151254

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved