A150999 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, 0), (1, -1, 0), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 38, 174, 800, 3798, 18079, 87274, 422415, 2059680, 10064422, 49389115, 242777149, 1196585692, 5905460251, 29196695458, 144498323490, 716025773879, 3550975915698, 17626078832477, 87547432848604, 435132850064506, 2163832245029922, 10765847763966771, 53586144482555603, 266827917734888510

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, -1 + 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] + aux[1 + i, 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: A150996 A150997 A150998 * A151000 A151001 A151002

Adjacent sequences: A150996 A150997 A150998 * A151000 A151001 A151002

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved