A150390 - OEIS

A150390

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

1, 2, 7, 24, 89, 330, 1275, 4877, 19070, 74212, 292166, 1147845, 4537572, 17923038, 71069941, 281673376, 1119180841, 4445898817, 17690888432, 70390284589, 280390365698, 1116936486403, 4452806146186, 17752863947281, 70818187733116, 282525417142847, 1127578132335156, 4500629627970806

(list; graph; refs; listen; history; text; internal format)

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[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + 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: A221454 A151293 A122446 * A052705 A150391 A150392

Adjacent sequences: A150387 A150388 A150389 * A150391 A150392 A150393

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved