A149565 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), (-1, 1, 1), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 13, 59, 197, 921, 3331, 15865, 60727, 290267, 1154275, 5560547, 22622223, 109636859, 454582257, 2209362255, 9300526153, 45349547541, 193067942897, 943931822673, 4058053450409, 19874749597221, 86155750783929, 422686506792649, 1844846909082093, 9064441951114577, 39801583197772329

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, 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, 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: A149562 A149563 A149564 * A149566 A298066 A298715

Adjacent sequences: A149562 A149563 A149564 * A149566 A149567 A149568

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved