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A150647 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, 1, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1)} 0
1, 2, 7, 28, 117, 509, 2279, 10366, 47724, 222280, 1043551, 4929582, 23413629, 111722678, 535090212, 2570945247, 12388203875, 59841383394, 289679576866, 1404971597312, 6826074319176, 33215354074742, 161846678561509, 789618624113747, 3856821700125396, 18857888173446861, 92293743446831249 (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[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A061539 A232970 A116078 * A150648 A150649 A090317

Adjacent sequences:  A150644 A150645 A150646 * A150648 A150649 A150650

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified December 5 13:23 EST 2016. Contains 278767 sequences.