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A150083 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, -1), (1, 0, 0)} 0
1, 2, 6, 19, 64, 231, 870, 3381, 13486, 54572, 224125, 933929, 3936544, 16765384, 71980646, 311017381, 1352436222, 5916084672, 26018810746, 114980517626, 510144652268, 2271483627590, 10149077070927, 45495648807256, 204569352272940, 922360752757352, 4168790748795270, 18884057836684121 (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, k, -1 + n] + aux[i, -1 + j, 1 + 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: A181734 A216447 A069728 * A220065 A047016 A307354

Adjacent sequences:  A150080 A150081 A150082 * A150084 A150085 A150086

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 24 02:57 EDT 2020. Contains 337315 sequences. (Running on oeis4.)