A151455 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 0), (0, -1), (0, 1), (1, 0), (1, 1)}.

1, 1, 4, 11, 41, 148, 572, 2267, 9162, 37891, 158433, 672432, 2879455, 12450139, 54227938, 237810937, 1049050916, 4651766238, 20724281904, 92714185721, 416353436502, 1876119867850, 8480415869145, 38442520244193, 174720912665199, 796023531740341, 3634755946489895, 16631145589921509

Offset

0,3

Links

Table of n, a(n) for n=0..27.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A121092 A281346 A030981 * A149269 A149270 A306188

Adjacent sequences: A151452 A151453 A151454 * A151456 A151457 A151458

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved