A151449 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, 0, 2, 4, 18, 46, 214, 742, 3146, 12162, 51862, 214090, 921302, 3937074, 17192430, 75188002, 332778382, 1478794218, 6622770990, 29791504178, 134763557054, 612115880722, 2792465318950, 12785429645706, 58747776081670, 270792162028674, 1251949437110774, 5804003443798442, 26976870402858422

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, -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: A064723 A301620 A240316 * A045664 A106520 A301802

Adjacent sequences: A151446 A151447 A151448 * A151450 A151451 A151452

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved