A151469 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, 0), (-1, 1), (0, 1), (1, -1), (1, 1)}.

1, 1, 4, 12, 55, 224, 1054, 4855, 23764, 116491, 587824, 2988264, 15439018, 80389938, 422931343, 2240237896, 11953324634, 64141694737, 346092872529, 1876152637561, 10215165278984, 55833837924973, 306268569253825, 1685420531789073, 9302712249561453, 51486848030764303, 285680988543516211

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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

Crossrefs

Sequence in context: A149418 A149419 A367450 * A268408 A092576 A149420

Adjacent sequences: A151466 A151467 A151468 * A151470 A151471 A151472

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved