A149359 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, -1), (1, -1, 0), (1, 0, 1)}.

1, 1, 4, 12, 43, 164, 640, 2610, 10853, 46147, 198963, 869969, 3847766, 17166855, 77287041, 350280733, 1597749772, 7329614871, 33785010841, 156445491596, 727303985933, 3393480786653, 15886260895083, 74591886573651, 351213344906583, 1657862411871953, 7844085620080768, 37194565658658818

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, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + 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: A149356 A149357 A149358 * A259223 A167402 A320643

Adjacent sequences: A149356 A149357 A149358 * A149360 A149361 A149362

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved