A149581 - OEIS

A149581

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

1, 1, 5, 15, 53, 201, 773, 2931, 11729, 46807, 187335, 762821, 3124945, 12808863, 52974987, 220149043, 916268057, 3831280947, 16081745835, 67615084323, 285092046863, 1205489408461, 5105695775689, 21666537365021, 92139791974945, 392421722005823, 1673781863814147, 7150683015163675

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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[i, j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + 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: A034537 A318493 A335025 * A149582 A149583 A149584

Adjacent sequences: A149578 A149579 A149580 * A149582 A149583 A149584

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved