A149949 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, 0), (0, 1, 0), (0, 1, 1), (1, 0, -1)}

1, 2, 5, 15, 50, 175, 643, 2442, 9497, 37772, 152757, 626466, 2602060, 10918685, 46235865, 197396778, 848640258, 3671712505, 15976961310, 69874586990, 307024031593, 1354759662530, 6001007238525, 26676880710809, 118977537295689, 532239704904251, 2387650011379440, 10739032580822009

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Alin Bostan and Manuel Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.

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, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A093129 A020876 A228343 * A149950 A370801 A024718

Adjacent sequences: A149946 A149947 A149948 * A149950 A149951 A149952

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved