A151421 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, -1), (-1, 0), (-1, 1), (0, 1), (1, 0)}.

1, 1, 3, 9, 28, 98, 346, 1275, 4783, 18309, 71087, 279361, 1109452, 4443790, 17935281, 72859781, 297693439, 1222522463, 5043272843, 20889707738, 86844446667, 362237124633, 1515497446739, 6357938199349, 26740979111391, 112733015296342, 476278051548456, 2016215519208030, 8551039079225071

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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

Crossrefs

Sequence in context: A148931 A243599 A148932 * A148933 A148934 A148935

Adjacent sequences: A151418 A151419 A151420 * A151422 A151423 A151424

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved