A148882 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), (0, 1, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 30, 97, 377, 1371, 5629, 21821, 91723, 370448, 1590614, 6610572, 28808574, 122283013, 539341238, 2326254276, 10357685562, 45242780800, 203008539599, 895866873466, 4045650433086, 18004733886152, 81746353342155, 366389377051723, 1671148718301495, 7535350327876314, 34505732112730067

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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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: A148879 A148880 A148881 * A148883 A148884 A148885

Adjacent sequences: A148879 A148880 A148881 * A148883 A148884 A148885

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved