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A150899 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, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)} 0
1, 2, 8, 34, 158, 734, 3522, 16931, 82554, 403038, 1981441, 9752204, 48182790, 238274637, 1180966793, 5857505302, 29093385069, 144585962175, 719208130384, 3579154241329, 17822841278776, 88782972903383, 442460346577831, 2205683206949191, 10998978955143953, 54860627855107552, 273700020776978268 (list; graph; refs; listen; history; text; internal format)
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, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150896 A150897 A150898 * A150900 A084207 A151305

Adjacent sequences:  A150896 A150897 A150898 * A150900 A150901 A150902

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)