A151445 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), (1, -1), (1, 0), (1, 1)}.

1, 1, 2, 6, 16, 49, 165, 538, 1881, 6673, 23954, 87931, 326739, 1224662, 4649697, 17778696, 68513483, 265907818, 1038089219, 4074688736, 16076107171, 63703583554, 253492204031, 1012528480799, 4058431546038, 16319598817463, 65820404923113, 266202737052052, 1079421216584541, 4387508855164279

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + 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: A052890 A052814 A192401 * A213429 A195645 A000136

Adjacent sequences: A151442 A151443 A151444 * A151446 A151447 A151448

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved