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A148190 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, 0), (0, 1, 0), (1, -1, 0), (1, 1, -1)} 0
1, 1, 2, 4, 12, 30, 99, 293, 1044, 3407, 12855, 44919, 176474, 649372, 2629712, 10070299, 41769656, 165069542, 698089371, 2829957804, 12160768699, 50345664661, 219252800095, 923848427883, 4069175264385, 17404407118104, 77409162199404, 335367168975910, 1504255075382674, 6589914030388130 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 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: A148187 A148188 A148189 * A151434 A296292 A287966

Adjacent sequences:  A148187 A148188 A148189 * A148191 A148192 A148193

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 30 12:03 EDT 2020. Contains 334724 sequences. (Running on oeis4.)