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A149881 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, 0, 1), (0, 0, 1), (0, 1, 0), (1, 0, -1)} 0
1, 2, 5, 14, 43, 147, 517, 1903, 7130, 27368, 107152, 425071, 1714426, 6973676, 28706751, 119063914, 497817611, 2096560172, 8878947340, 37844245609, 162013011858, 697185486077, 3012184036012, 13066185648559, 56890967243092, 248488701339287, 1089017528771118, 4785544357915749 (list; graph; refs; listen; history; text; internal format)
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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A122993 A137552 A137553 * A148334 A149882 A137554

Adjacent sequences:  A149878 A149879 A149880 * A149882 A149883 A149884

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)