A150371 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, 1, 0), (1, 0, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 23, 94, 370, 1604, 6727, 30370, 133713, 615882, 2777178, 13009742, 59927580, 283460002, 1321621492, 6307233267, 29747482950, 142758158057, 678127146675, 3271810279782, 15650954143844, 75782175561207, 364187983535248, 1769609725577321, 8543602251222249, 41615832882726956, 201560940547506289

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, 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, 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: A150368 A150369 A150370 * A150372 A150373 A150374

Adjacent sequences: A150368 A150369 A150370 * A150372 A150373 A150374

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved