A149345 - OEIS

A149345

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, 0), (0, -1, 0), (0, 1, -1), (0, 1, 1), (1, 1, -1)}.

1, 1, 4, 12, 42, 149, 563, 2167, 8521, 34010, 137899, 566278, 2347387, 9815176, 41356830, 175507147, 749312195, 3216195084, 13872335903, 60105398885, 261496852724, 1141895019478, 5003444985964, 21993343270089, 96961107283936, 428639320358383, 1899717847605466, 8439559063692215

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A178078 A135489 A100217 * A149346 A149347 A173411

Adjacent sequences: A149342 A149343 A149344 * A149346 A149347 A149348

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved