A148314 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), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 5, 14, 38, 118, 353, 1142, 3628, 12070, 39764, 135114, 456160, 1574734, 5412457, 18912486, 65896108, 232472470, 818693712, 2910776906, 10338854570, 36996327526, 132328613972, 476099847330, 1712816375654, 6191107090798, 22382207179178, 81226673300290, 294879429959828, 1073880052595966

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, -1 + 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: A006574 A053419 A079227 * A001011 A148315 A331573

Adjacent sequences: A148311 A148312 A148313 * A148315 A148316 A148317

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved