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A150897 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, 0, 1), (0, -1, 1), (0, 0, 1), (1, 1, -1), (1, 1, 1)} 0
1, 2, 8, 34, 156, 718, 3422, 16334, 79118, 384020, 1878350, 9201068, 45268796, 223004070, 1101463614, 5445866142, 26971500686, 133688792364, 663414638696, 3294250138924, 16371243474378, 81401390498830, 404986420868284, 2015720354009970, 10037249760011008, 49997200939602922, 249130467399797802 (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, -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, -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: A150894 A150895 A150896 * A150898 A150899 A150900

Adjacent sequences:  A150894 A150895 A150896 * A150898 A150899 A150900

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified June 26 19:25 EDT 2022. Contains 354885 sequences. (Running on oeis4.)