A151345 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 1)}.

1, 1, 6, 55, 644, 8694, 128964, 2045901, 34136960, 592493044, 10614366568, 195164993478, 3667395504304, 70199379387700, 1365217425954360, 26918993235702735, 537238205832405960, 10837199420262489120, 220699085927921277600, 4533022083670853217060, 93823829712145743930720

Offset: 0

Author

Manuel Kauers, Nov 18 2008

Keywords

• nonn
• walk

Links

• M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.

Crossrefs

Cf. A151341, A151343, A151344.

Programs

Maple

ogf := subs(t=sqrt(x), series(Int(Int(2*hypergeom([3/4, 5/4],[2],64*t^2*(t^2+1)/(16*t^2+1)^2)/(16*t^2+1)^(3/2),t),t)/t^2, t=0,60)); # Mark van Hoeij, Aug 17 2014

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[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, 2 n], {n, 0, 25}]