A150735 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, 0, 0), (0, 0, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 29, 122, 514, 2254, 10027, 45410, 207523, 959224, 4462832, 20905920, 98460678, 465872363, 2213026310, 10550448654, 50449683620, 241900053918, 1162722150227, 5600826084749, 27031981353774, 130701240726542, 632959008475626, 3069796368448293, 14908391354774898, 72491332397240089

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A345131 A150733 A150734 * A150736 A150737 A150738

Adjacent sequences: A150732 A150733 A150734 * A150736 A150737 A150738

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved