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A150781 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, 0), (1, 0, -1), (1, 0, 0), (1, 1, 1)} 0
1, 2, 8, 30, 134, 558, 2598, 11482, 54330, 247658, 1185087, 5507642, 26549870, 125054453, 605935016, 2881536153, 14016692100, 67135696027, 327558404737, 1577649495853, 7715950487797, 37326948831287, 182917862593182, 888045302300415, 4358927495843082, 21224253595654626, 104322256244653467 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150778 A150779 A150780 * A150782 A150783 A150784

Adjacent sequences:  A150778 A150779 A150780 * A150782 A150783 A150784

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 21 15:18 EDT 2021. Contains 348155 sequences. (Running on oeis4.)