A151333 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 1), (0, 1), (1, -1)}.

1, 0, 2, 6, 42, 308, 2424, 21118, 194010, 1866896, 18674908, 192737280, 2042585592, 22142680360, 244772420336, 2752312897942, 31415853441050, 363394473652344, 4253708877703476, 50326069309616132, 601181906802967564, 7244698219481190376, 88003741534163878912, 1076851417694238454896

Offset

0,3

Links

Table of n, a(n) for n=0..23.

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 11, Tag 19

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[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, 2 n], {n, 0, 25}]

Crossrefs

Sequence in context: A156437 A127071 A353994 * A190626 A191975 A074015

Adjacent sequences: A151330 A151331 A151332 * A151334 A151335 A151336

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved