A150945 - OEIS

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A150945

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

1, 2, 9, 35, 149, 665, 2986, 13538, 62963, 292567, 1369313, 6478437, 30684591, 145862057, 697855915, 3341734742, 16041352603, 77313798602, 372938012558, 1802009845814, 8731012176788, 42333931038548, 205525434047243, 999741145885366, 4866158320971535, 23708995049288776, 115682290686505748

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A077837 A289974 A289782 * A150946 A150947 A110224

Adjacent sequences: A150942 A150943 A150944 * A150946 A150947 A150948

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved