A149959 - OEIS

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A149959

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

1, 2, 5, 16, 54, 180, 634, 2288, 8237, 30257, 112414, 417790, 1568921, 5928140, 22414805, 85285035, 325751694, 1245081641, 4778408244, 18387308367, 70800124423, 273382643467, 1057644337911, 4094204572221, 15881018461005, 61689691110754, 239765157267667, 933288825944631, 3636898463404796

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

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..28.

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, -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: A081126 A018191 A006191 * A161941 A120899 A149960

Adjacent sequences: A149956 A149957 A149958 * A149960 A149961 A149962

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved