A150764 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, -1, 0), (1, 0, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 30, 126, 530, 2330, 10290, 46410, 210462, 966042, 4455066, 20703606, 96597930, 453102078, 2132350506, 10074190698, 47726505398, 226781353370, 1080087917766, 5156365273202, 24664826475302, 118210918387146, 567495368954410, 2728811135183302, 13140420242879490, 63364479984294270

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-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, 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: A054663 A150763 A054662 * A150765 A150766 A150767

Adjacent sequences: A150761 A150762 A150763 * A150765 A150766 A150767

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved