A150012 - OEIS

A150012

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

1, 2, 5, 17, 65, 237, 903, 3626, 14822, 60668, 252632, 1066726, 4542198, 19459068, 83952935, 364404201, 1590499390, 6973481584, 30691951800, 135582966112, 601142785215, 2673652685169, 11922615242208, 53301912197676, 238892225367457, 1073099767854329, 4829893177660861, 21779307506270372

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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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + 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: A109084 A217596 A090902 * A150013 A052539 A123166

Adjacent sequences: A150009 A150010 A150011 * A150013 A150014 A150015

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved