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A150904 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, -1), (-1, -1, 1), (-1, 0, 1), (1, 1, 0), (1, 1, 1)} 0
1, 2, 9, 29, 141, 518, 2559, 10010, 49737, 201902, 1006037, 4186127, 20888571, 88476550, 441843335, 1896865677, 9477117035, 41119442928, 205497571867, 899303209251, 4495102858063, 19812021068060, 99039630904031, 439142783921982, 2195411967657091, 9784682586251586, 48918892448735361 (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, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A150902 A150903 A151306 * A122675 A042357 A079783

Adjacent sequences:  A150901 A150902 A150903 * A150905 A150906 A150907

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified December 1 11:07 EST 2021. Contains 349429 sequences. (Running on oeis4.)