A149950 - OEIS

A149950

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, 0), (0, 1, 0), (0, 1, 1), (1, 0, -1)}

1, 2, 5, 15, 50, 175, 643, 2442, 9497, 37772, 152799, 626592, 2602438, 10922440, 46249757, 197449903, 848960606, 3672993876, 15982347311, 69901749199, 307137650010, 1355254986715, 6003323405960, 26686855461722, 119021651507968, 532439628200272, 2388526982109443, 10742935351026098

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OFFSET

0,2

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 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: A020876 A228343 A149949 * A370801 A024718 A149951

Adjacent sequences: A149947 A149948 A149949 * A149951 A149952 A149953

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved