A151452 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), (1, -1), (1, 1)}.

1, 1, 3, 9, 35, 123, 495, 1989, 8309, 35051, 151437, 659819, 2913973, 12976939, 58299997, 263670833, 1200259447, 5492958255, 25263912743, 116702563415, 541237283707, 2519080782283, 11762908211343, 55090441132491, 258716199460163, 1218036100384603, 5747824726594467, 27181821363396903

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, 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: A149013 A149014 A149015 * A149016 A149017 A149018

Adjacent sequences: A151449 A151450 A151451 * A151453 A151454 A151455

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved