A148953 - OEIS

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A148953

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

1, 1, 3, 9, 30, 103, 384, 1442, 5630, 22140, 89391, 362567, 1496206, 6200980, 26010002, 109530531, 465203693, 1983050889, 8507197775, 36615589619, 158370065466, 686997801100, 2991781230521, 13062875230227, 57217563779248, 251205593841622, 1105814802393350, 4877926862758847, 21565940667871892

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

OFFSET

0,3

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, 1 + k, -1 + n] + aux[i, 1 + 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: A047007 A007453 A148952 * A148954 A289602 A148955

Adjacent sequences: A148950 A148951 A148952 * A148954 A148955 A148956

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved