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A149871 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, -1), (0, 1, 0), (0, 1, 1), (1, -1, -1)} 0
1, 2, 5, 13, 42, 138, 482, 1674, 6193, 22905, 87302, 332124, 1300396, 5086323, 20241313, 80532296, 325512139, 1315265248, 5373186309, 21959388097, 90618415683, 374030443628, 1555349602195, 6471926603762, 27103293936363, 113566464857234, 478365524549750, 2016520963230236, 8538774214340379 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..28.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + 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: A262934 A149869 A149870 * A149872 A149873 A149874

Adjacent sequences:  A149868 A149869 A149870 * A149872 A149873 A149874

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 21 12:11 EST 2019. Contains 329370 sequences. (Running on oeis4.)