A151373 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, 0), (1, 1)}.

1, 0, 3, 5, 30, 111, 548, 2586, 13087, 67422, 356949, 1926267, 10572832, 58881097, 332036571, 1893134282, 10898885385, 63289478066, 370367463568, 2182496117488, 12942151954077, 77187058254066, 462756053380104, 2787666781698785, 16867270687964194, 102474811093369802, 624924032105488251

Offset

0,3

Links

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

A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 54.

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

Crossrefs

Sequence in context: A341037 A181429 A162262 * A189739 A035410 A290487

Adjacent sequences: A151370 A151371 A151372 * A151374 A151375 A151376

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved