A148947 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, 0, 0), (-1, 0, 1), (0, -1, 0), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 9, 30, 100, 374, 1388, 5432, 21140, 85814, 346706, 1441436, 5968072, 25281324, 106700835, 458490321, 1963661842, 8535636877, 36992407718, 162318727824, 710304997081, 3141342032407, 13857989184695, 61696721357473, 274043373954929, 1227052589416842, 5482416359215794, 24670026546816835

Offset

0,3

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A089931 A148946 A096222 * A090573 A228339 A257641

Adjacent sequences: A148944 A148945 A148946 * A148948 A148949 A148950

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved