A151459 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, -1), (1, 1)}.

1, 1, 3, 9, 31, 110, 417, 1610, 6443, 26109, 108187, 452431, 1920684, 8211507, 35485309, 154206122, 675502094, 2972505787, 13161176353, 58492256069, 261228659937, 1170349516612, 5264116418017, 23741320362089, 107423324472193, 487191992942365, 2215574902892336, 10096007665376051, 46112513697390089

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, -1 + j, -1 + n] + aux[-1 + i, 1 + 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: A112566 A128082 A148970 * A151033 A047012 A120305

Adjacent sequences: A151456 A151457 A151458 * A151460 A151461 A151462

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved