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A148376 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, -1), (0, -1, 1), (0, 0, 1), (1, 1, -1)} 0
1, 1, 2, 5, 16, 46, 153, 513, 1852, 6544, 24235, 91027, 348827, 1338838, 5247023, 20764179, 82790176, 332119886, 1347341002, 5497739594, 22536585590, 92940614967, 385805282451, 1607498598645, 6723421275983, 28257224994831, 119243377085374, 504612923309747, 2142551689248165 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A148375 A075887 A306504 * A148377 A349270 A163865

Adjacent sequences:  A148373 A148374 A148375 * A148377 A148378 A148379

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 2 06:08 EDT 2022. Contains 357191 sequences. (Running on oeis4.)