A151448 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), (0, 1), (1, 1)}.

1, 1, 4, 13, 46, 178, 699, 2826, 11665, 48877, 207426, 889753, 3850726, 16792923, 73721417, 325516893, 1444683024, 6440892041, 28832816045, 129544987197, 583978531063, 2640502004594, 11972283977009, 54421442961369, 247958522736954, 1132210929270549, 5180203300927992, 23745237667125709

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[i, -1 + 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: A087440 A149437 A149438 * A218667 A149439 A014145

Adjacent sequences: A151445 A151446 A151447 * A151449 A151450 A151451

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved