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A149664 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, 0, 0), (0, -1, 1), (0, 0, -1), (1, 1, 1)} 0
1, 1, 5, 17, 61, 249, 1003, 4115, 17371, 73519, 315575, 1367431, 5946949, 26092679, 115017031, 508924409, 2263672565, 10098869293, 45205624797, 203017643007, 913862154449, 4124692123161, 18658670407501, 84569931164973, 384100732416711, 1747491307163059, 7963465982266133, 36348101856151661 (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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A273759 A149662 A149663 * A149665 A149666 A273327

Adjacent sequences:  A149661 A149662 A149663 * A149665 A149666 A149667

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 29 04:33 EDT 2020. Contains 334697 sequences. (Running on oeis4.)