A151352 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), (0, 1), (1, 0)}.

1, 0, 1, 2, 2, 13, 21, 67, 231, 509, 1947, 5522, 16637, 58030, 170547, 579290, 1896475, 6081303, 20884509, 68398930, 231286693, 788124656, 2649341358, 9130259705, 31203913903, 107304612514, 372144639423, 1285741209096, 4480102404983, 15625089552273, 54591352088818, 191664831925204, 673088362068478

Offset

0,4

Links

Table of n, a(n) for n=0..32.

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 3, Tag 6

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, j, -1 + n] + aux[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: A347080 A141575 A306738 * A155915 A173466 A151367

Adjacent sequences: A151349 A151350 A151351 * A151353 A151354 A151355

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved