A151415 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, 0), (1, 1)}.

1, 0, 2, 3, 10, 27, 89, 267, 868, 2858, 9510, 31830, 108638, 373219, 1288064, 4482534, 15710368, 55258931, 195240700, 693284513, 2470263132, 8827776270, 31654190580, 113835950410, 410335021648, 1482638356348, 5369592056146, 19484896375080, 70835100481126, 257981797359638, 941120763934455, 3438343699103345

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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: A238937 A278088 A052929 * A134588 A000060 A089752

Adjacent sequences: A151412 A151413 A151414 * A151416 A151417 A151418

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved