A151351 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), (1, -1), (1, 1)}.

1, 0, 1, 1, 8, 18, 90, 301, 1413, 5628, 26083, 114133, 536065, 2475101, 11844488, 56598072, 275910093, 1350392157, 6692423872, 33348850521, 167631991925, 847255772901, 4310527391729, 22040709981279, 113295384193957, 584965125869980, 3033583060169821, 15793448306316644, 82532818466952627

Offset

0,5

Links

Table of n, a(n) for n=0..28.

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 52

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[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: A120543 A337836 A036747 * A354769 A113563 A173734

Adjacent sequences: A151348 A151349 A151350 * A151352 A151353 A151354

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved