A151369 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, 0), (1, 1)}.

1, 0, 2, 3, 15, 51, 208, 893, 3841, 17564, 80641, 381664, 1829908, 8912028, 43963132, 219194931, 1104020412, 5607960015, 28711787341, 148026751064, 768028849708, 4007925077375, 21025463025330, 110833046059230, 586841075931626, 3119986329482438, 16650738818854660, 89175505308627426, 479163215916007973

Offset

0,3

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 44, Tag 50.

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[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: A048076 A203432 A298409 * A143885 A172012 A323709

Adjacent sequences: A151366 A151367 A151368 * A151370 A151371 A151372

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved