A148090 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), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 10, 24, 74, 214, 695, 2166, 7106, 23361, 80689, 278290, 986215, 3470804, 12422826, 44857992, 164333810, 605851165, 2248012785, 8356195207, 31310333219, 118096170532, 448467623116, 1710002315918, 6536696182906, 25065265795150, 96586728914920, 373879518394390, 1452827184593812, 5658040612566495

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 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, 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: A200743 A061055 A060776 * A148091 A123420 A000458

Adjacent sequences: A148087 A148088 A148089 * A148091 A148092 A148093

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved