A150463 - OEIS

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A150463

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

1, 2, 7, 25, 97, 398, 1679, 7288, 32223, 144618, 657031, 3014433, 13946921, 64978210, 304552559, 1434806969, 6790079675, 32260223432, 153804362391, 735548808541, 3527375302589, 16957713624004, 81705722271403, 394471543356170, 1907993817660033, 9244134602541970, 44856136835227851, 217966184541636587

(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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A150460 A150461 A150462 * A150464 A150465 A150466

Adjacent sequences: A150460 A150461 A150462 * A150464 A150465 A150466

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved