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A148056 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, -1, 1), (-1, 1, 0), (0, 0, -1), (1, 0, 0)} 0
1, 1, 2, 3, 10, 22, 65, 152, 509, 1466, 4645, 13532, 44434, 146454, 483958, 1573257, 5245446, 18189431, 62918036, 215842095, 743114400, 2625979396, 9395162641, 33370716692, 118291958507, 424227452507, 1546163643295, 5636678152183, 20454730175647, 74489593325489, 274498234923989, 1018318442708743 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A113202 A079078 A285794 * A148057 A148058 A148059

Adjacent sequences:  A148053 A148054 A148055 * A148057 A148058 A148059

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 16 12:41 EDT 2019. Contains 327113 sequences. (Running on oeis4.)