A151079 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), (-1, 0, -1), (0, 1, 1), (1, 0, 0), (1, 0, 1)}.

1, 3, 10, 41, 168, 727, 3219, 14385, 65613, 300679, 1392830, 6492134, 30415783, 143309584, 677504561, 3216099178, 15311310131, 73103177454, 349911386579, 1678491213789, 8068384917616, 38852770111657, 187412268123453, 905363554615997, 4379869444310765, 21215628878755604, 102888394500800977

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A149057 A149058 A151078 * A151080 A153474 A151081

Adjacent sequences: A151076 A151077 A151078 * A151080 A151081 A151082

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved