A151473 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, -1), (-1, 0), (0, -1), (0, 1), (1, -1), (1, 1)}.

1, 1, 4, 12, 49, 198, 863, 3884, 17975, 85334, 412190, 2024852, 10077117, 50742026, 258072225, 1324122267, 6846977215, 35650800062, 186783189059, 984088270530, 5211141864900, 27722794111428, 148106868818943, 794324000203226, 4275354972290547, 23087757785665053, 125061096159246886, 679360863935385860

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, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A013935 A149386 A149387 * A152123 A149388 A149389

Adjacent sequences: A151470 A151471 A151472 * A151474 A151475 A151476

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved