A150662 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, 0, 1), (0, -1, 1), (0, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 29, 125, 562, 2597, 12210, 58097, 279086, 1350199, 6567293, 32080325, 157251140, 772958093, 3808104405, 18796934995, 92929725778, 460047738803, 2280054707147, 11311248677395, 56161619393806, 279051051744105, 1387400623154992, 6901759158188955, 34350115522554034, 171033917741551369

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, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A120757 A134169 A052961 * A278391 A126568 A150663

Adjacent sequences: A150659 A150660 A150661 * A150663 A150664 A150665

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved