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A149486 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, 0, 1), (-1, 1, 1), (1, -1, 0), (1, 0, 1), (1, 1, -1)}. 0
1, 1, 4, 13, 59, 237, 1117, 4876, 23484, 107063, 521987, 2442075, 11995134, 57056591, 281598695, 1354666528, 6707399025, 32526399379, 161411737737, 787355791682, 3913582816735, 19175058749533, 95424679112641, 469146070330091, 2336818911143639, 11519647002903261, 57419336864686471, 283663564494396519 (list; graph; refs; listen; history; text; internal format)
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[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A158267 A219572 A026663 * A317891 A115455 A241470

Adjacent sequences:  A149483 A149484 A149485 * A149487 A149488 A149489

KEYWORD

nonn,walk,changed

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 1 10:54 EDT 2022. Contains 354972 sequences. (Running on oeis4.)