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A150661 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), (1, -1, 1), (1, 0, 0), (1, 1, -1)} 0
1, 2, 7, 28, 122, 555, 2588, 12277, 58913, 285117, 1388522, 6794467, 33370370, 164371665, 811518081, 4014028257, 19884948419, 98631030741, 489728806588, 2433756380645, 12103713123846, 60232647664468, 299900743554687, 1493904068893024, 7444581364893104, 37111414613600947, 185056883908261473 (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, 1 + 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: A293266 A150659 A150660 * A269228 A005435 A291091

Adjacent sequences:  A150658 A150659 A150660 * A150662 A150663 A150664

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified March 28 17:51 EDT 2020. Contains 333103 sequences. (Running on oeis4.)