A149953 - OEIS

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A149953

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

1, 2, 5, 15, 51, 183, 690, 2680, 10664, 43361, 179166, 750618, 3182815, 13627850, 58858838, 256136007, 1121888880, 4942820194, 21890082385, 97392793659, 435140490144, 1951512891396, 8782251791612, 39646601500866, 179495259553219, 814795429411189, 3707690621124339, 16909746064544733

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

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, j, 1 + k, -1 + n] + aux[i, -1 + 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, -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: A350490 A304386 A140639 * A149954 A149955 A374553

Adjacent sequences: A149950 A149951 A149952 * A149954 A149955 A149956

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved