A149291 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, 0), (-1, 0, 1), (-1, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 46, 145, 641, 2275, 10330, 38683, 179077, 698969, 3277788, 13154295, 62279600, 255360623, 1217775810, 5076594445, 24346635475, 102858261727, 495528611722, 2116511750627, 10234179952692, 44114208093693, 213964420670390, 929479716561285, 4519843635303271, 19766146842430959

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A074410 A359707 A363663 * A149292 A149293 A149294

Adjacent sequences: A149288 A149289 A149290 * A149292 A149293 A149294

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved