A150759 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, 0), (0, 0, -1), (0, 0, 1), (1, 1, 1)}

1, 2, 8, 30, 120, 504, 2126, 9170, 40044, 176044, 781600, 3490012, 15664056, 70669628, 320004610, 1454279906, 6630320468, 30309488628, 138910831512, 638073465476, 2936860540160, 13543141717064, 62559629953436, 289436485560372, 1341060883889256, 6221966893608856, 28903711416385792, 134427762081030024

Offset

0,2

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[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, 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: A155116 A133915 A370539 * A150760 A230588 A151303

Adjacent sequences: A150756 A150757 A150758 * A150760 A150761 A150762

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved