A151450 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, 0), (1, 1)}.

1, 0, 4, 5, 34, 98, 458, 1703, 7632, 31222, 139078, 601834, 2692054, 12000298, 54304846, 246205555, 1126480236, 5170553126, 23870651114, 110597543652, 514517316974, 2401300629466, 11243551419878, 52789725198754, 248514184071046, 1172682575616138, 5545963779654358, 26282130844530698

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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

Formula

G.f.: Int(Int(-2+Int(6*(1-9*x)*(1-Int(4*(1-2*x-15*x^2)^(3/2)*((1830*x^5+59*x^4+362*x^3+22*x^2-8*x+3)*(1-4*x^2)*hypergeom([7/4, 9/4],[2],64*x^3*(1+x)/(1-4*x^2)^2)+7*(750*x^4-307*x^3-213*x^2-45*x+11) *x^3*hypergeom([9/4, 11/4],[3],64*x^3*(1+x)/(1-4*x^2)^2))/((1-4*x^2)^(9/2)*(9*x-1)^2*(1+x)),x))/(1-2*x-15*x^2)^(5/2),x),x),x)/(x^2*(x-1)). - Mark van Hoeij, Aug 27 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, 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: A244333 A041907 A228662 * A243772 A332316 A243275

Adjacent sequences: A151447 A151448 A151449 * A151451 A151452 A151453

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved