A149738 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, 0), (1, -1, 0), (1, 1, -1), (1, 1, 1)}

1, 1, 5, 17, 77, 305, 1391, 5997, 27977, 125933, 595293, 2743171, 13083667, 61244179, 294145111, 1392517293, 6723830223, 32097784775, 155628202165, 747653078115, 3637006800251, 17559574813135, 85649555597893, 415170366061299, 2029579753816049, 9870089834877679, 48341005888737633, 235722964098344779

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A145959 A126956 A149737 * A149739 A149740 A149741

Adjacent sequences: A149735 A149736 A149737 * A149739 A149740 A149741

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved