A150386 - OEIS

A150386

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

1, 2, 7, 23, 100, 368, 1686, 6656, 31226, 127887, 609765, 2559417, 12319958, 52642465, 255233171, 1104774994, 5383290940, 23543707785, 115154181131, 507764596679, 2490990817895, 11058013965850, 54374327267962, 242750992541387, 1195937237740590, 5364847080376535, 26471952320243373, 119244489489488329

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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[1 + i, -1 + j, k, -1 + n] + aux[1 + 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: A150384 A150385 A047066 * A150387 A265797 A150388

Adjacent sequences: A150383 A150384 A150385 * A150387 A150388 A150389

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved