A149578 - OEIS

A149578

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

1, 1, 5, 15, 51, 211, 795, 3057, 13001, 52581, 213253, 925853, 3879469, 16223453, 71442225, 305928395, 1305276203, 5807259867, 25240311855, 109232894395, 489780437147, 2152075952175, 9413280045751, 42466522816087, 188164257550383, 829897208393779, 3762535997730743, 16782610498398015

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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[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A255442 A149576 A149577 * A149579 A149580 A099834

Adjacent sequences: A149575 A149576 A149577 * A149579 A149580 A149581

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved