A150290 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, 1, 1), (0, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 2, 6, 23, 93, 390, 1691, 7543, 34135, 156398, 725279, 3391133, 15954218, 75517827, 359295308, 1716021026, 8224494894, 39546508613, 190661813136, 921316365597, 4461549709532, 21646623010275, 105197107328215, 511998760462163, 2495386282301781, 12177034643251279, 59487864132277409, 290915495434027544

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A150289 A326355 A012866 * A150291 A150292 A191721

Adjacent sequences: A150287 A150288 A150289 * A150291 A150292 A150293

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved