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A149033 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, 0, 1), (0, 1, 1), (1, -1, 0), (1, 0, -1)} 0
1, 1, 3, 10, 34, 126, 491, 1949, 7919, 32903, 138223, 587746, 2526421, 10941149, 47729602, 209562569, 924878572, 4101835581, 18270356562, 81686164214, 366493225290, 1649478891641, 7444911031185, 33690982426856, 152831005271410, 694817195153960, 3165364902881297, 14447917905401121 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..27.

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A306409 A047032 A149032 * A149034 A149035 A099907

Adjacent sequences:  A149030 A149031 A149032 * A149034 A149035 A149036

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 18 14:41 EDT 2022. Contains 353816 sequences. (Running on oeis4.)