A151501 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 0), (-1, 1), (0, -1), (1, 0)}

1, 0, 2, 1, 8, 12, 45, 113, 341, 1018, 3095, 9555, 30324, 95537, 309763, 1002577, 3285362, 10859463, 36025440, 120586518, 405317722, 1369340161, 4651457133, 15854097472, 54284662488, 186521139750, 642995941300, 2224213237576, 7715127092600, 26838793844166, 93608792582527, 327272805790058, 1146930142662274

Offset

0,3

Links

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

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

Crossrefs

Sequence in context: A214278 A214279 A360608 * A102735 A088960 A263528

Adjacent sequences: A151498 A151499 A151500 * A151502 A151503 A151504

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved