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A151174 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, -1), (1, 0, 0), (1, 0, 1), (1, 1, 1)} 0
1, 3, 12, 49, 219, 971, 4499, 20679, 97652, 458010, 2187664, 10392377, 50018335, 239690199, 1159912997, 5593476880, 27178383256, 131685711649, 641876232929, 3121517496002, 15253605572885, 74398068178947, 364302080576825, 1781098822234544, 8736369426482435, 42797279032088982, 210226191534353452 (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, -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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A151172 A151173 A301456 * A151175 A151176 A151177

Adjacent sequences:  A151171 A151172 A151173 * A151175 A151176 A151177

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 26 10:17 EDT 2022. Contains 354086 sequences. (Running on oeis4.)