A149066 - OEIS

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A149066

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

1, 1, 3, 11, 41, 165, 693, 2975, 13102, 58543, 265533, 1216437, 5625630, 26208715, 122883878, 579308565, 2743787003, 13048731447, 62277382336, 298169598323, 1431550417591, 6890222494696, 33237555228170, 160656725334807, 777962747662943, 3773430268357265, 18330224672912397, 89165583321567972

(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[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A027103 A151086 A151087 * A149067 A018962 A102417

Adjacent sequences: A149063 A149064 A149065 * A149067 A149068 A149069

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved