A149626 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, 1), (1, -1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 67, 247, 1115, 4489, 20413, 86161, 393981, 1711377, 7860333, 34797749, 160412561, 719666043, 3327831031, 15076408631, 69900784059, 319040043727, 1482638099379, 6806476537095, 31695626200787, 146186884073611, 681985625875943, 3157451376658283, 14754091284261159, 68524787682712427

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A149623 A149624 A149625 * A149627 A149628 A149629

Adjacent sequences: A149623 A149624 A149625 * A149627 A149628 A149629

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved