A150676 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, 0), (-1, 0, -1), (0, -1, -1), (0, 1, 1), (1, 1, 1)}.

1, 2, 8, 26, 112, 426, 1866, 7680, 33800, 145584, 644204, 2849608, 12708082, 57072764, 256787282, 1163494774, 5279181198, 24062021656, 109946406784, 503537243732, 2313217721510, 10640187026118, 49078644674492, 226638419576674, 1048737487188412, 4859531391937962, 22548475250472276, 104782363038529372

Offset

0,2

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A187151 A150674 A150675 * A150677 A150678 A150679

Adjacent sequences: A150673 A150674 A150675 * A150677 A150678 A150679

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved