A150703 - OEIS

A150703

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

1, 2, 8, 26, 122, 448, 2152, 8472, 41248, 168404, 828858, 3464842, 17127182, 72901650, 361432694, 1558479474, 7746534534, 33739814458, 167937821994, 737581929028, 3675011084182, 16249861680214, 81036758007684, 360353356263648, 1798049012385234, 8034835078945374, 40108334713352168, 179984972592034232

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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, 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: A150700 A150701 A150702 * A150704 A150705 A150706

Adjacent sequences: A150700 A150701 A150702 * A150704 A150705 A150706

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved