A150752 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, 0, 0), (1, 1, -1), (1, 1, 1)}

1, 2, 8, 29, 127, 528, 2411, 10620, 49681, 225880, 1071866, 4971414, 23805922, 111917754, 539344010, 2560334329, 12397503180, 59283008091, 288120270613, 1385564822863, 6753740190330, 32625131639352, 159405606486602, 772854679955346, 3783607449342410, 18399656695874309, 90227724041309335

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 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: A150749 A150750 A150751 * A150753 A162066 A151302

Adjacent sequences: A150749 A150750 A150751 * A150753 A150754 A150755

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved