A151335 - OEIS

A151335

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

1, 0, 0, 1, 0, 1, 5, 1, 18, 43, 47, 313, 570, 1480, 5847, 11715, 41194, 124918, 317707, 1120909, 3159179, 9581991, 31624946, 92407981, 300936377, 954921610, 2965630143, 9769316877, 30986916602, 100406899586, 329864837841, 1066298792633, 3525879988702, 11612179660287, 38300799541992, 127788972039783

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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 12

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

CROSSREFS

Sequence in context: A050400 A326121 A008971 * A297174 A226605 A055584

Adjacent sequences: A151332 A151333 A151334 * A151336 A151337 A151338

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved