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A150856 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, 0), (0, -1, 1), (0, 1, 1), (1, 1, -1), (1, 1, 0)} 0
1, 2, 8, 32, 141, 636, 2940, 13823, 65721, 315216, 1522515, 7391165, 36038108, 176319221, 865083102, 4254538369, 20965316148, 103485337461, 511540876219, 2531710079069, 12543258149487, 62202589129637, 308714505509069, 1533253924270778, 7619784221149331, 37888871898194684, 188492641232047703 (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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150853 A150854 A150855 * A105483 A150857 A150858

Adjacent sequences:  A150853 A150854 A150855 * A150857 A150858 A150859

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 23 16:29 EST 2022. Contains 350514 sequences. (Running on oeis4.)