A151460 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), (0, -1), (0, 1), (1, 0), (1, 1)}.

1, 1, 4, 12, 44, 164, 643, 2574, 10554, 43956, 185642, 792846, 3418616, 14860606, 65054182, 286536007, 1268905654, 5646284864, 25232338903, 113194654758, 509574041184, 2301247205497, 10422542804458, 47329681905633, 215452103352557, 982977683341317, 4494071645187763, 20586153075994492

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[i, 1 + 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: A149362 A149363 A188632 * A149364 A055542 A149365

Adjacent sequences: A151457 A151458 A151459 * A151461 A151462 A151463

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved