A149582 - OEIS

A149582

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

1, 1, 5, 15, 53, 201, 773, 2963, 11761, 47159, 189735, 770225, 3158973, 12996675, 53710019, 223130215, 930787997, 3892415935, 16331509667, 68731845575, 289927401743, 1225576064229, 5192389009213, 22041829282085, 93722873387617, 399177559960043, 1702848666121575, 7274406498614907

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OFFSET

0,3

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, -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, 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: A318493 A335025 A149581 * A149583 A149584 A147324

Adjacent sequences: A149579 A149580 A149581 * A149583 A149584 A149585

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved