A151439 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), (-1, 1), (0, 1), (1, -1), (1, 0)}.

1, 1, 2, 7, 22, 74, 269, 1022, 3987, 15897, 64787, 268685, 1130049, 4810797, 20700879, 89918115, 393811281, 1737451533, 7716025961, 34470611627, 154822298289, 698772455153, 3167909310263, 14420624239207, 65891331074973, 302120467333277, 1389723243292295, 6411702376827157, 29663748424179837

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, 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, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A307976 A114495 A137398 * A204218 A007141 A278151

Adjacent sequences: A151436 A151437 A151438 * A151440 A151441 A151442

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved