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A151195 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), (0, 1, -1), (0, 1, 1), (1, 0, 1), (1, 1, 0)} 0
1, 3, 12, 52, 237, 1099, 5213, 24940, 120389, 584838, 2853373, 13976063, 68652709, 338034589, 1667756201, 8241492662, 40782808665, 202049395507, 1002001335467, 4973396367842, 24703642321516, 122786278471416, 610640791721211, 3038355979978879, 15124580771488710, 75317942432483327 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A151194 A268208 A007856 * A151196 A010736 A151197

Adjacent sequences:  A151192 A151193 A151194 * A151196 A151197 A151198

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)