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A151430
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), (0, 1), (1, -1), (1, 0)}.
0
1, 1, 2, 7, 19, 61, 224, 771, 2855, 11005, 41963, 165661, 664443, 2674101, 10955892, 45281419, 188288455, 790957165, 3343062477, 14209485769, 60792612875, 261330644741, 1128597807923, 4896682653677, 21327006074731, 93233880458581, 409028951228459, 1800105977084221, 7946053746358811
OFFSET
0,3
LINKS
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(Int((1-9*x)*(6+12*Int((1-2*x-15*x^2)^(3/2)*((5-18*x-816*x^6 -832*x^5+288*x^4+128*x^3+71*x^2)*hypergeom([5/4, 7/4],[1],64*x^3*(1+x)/ (1-4*x^2)^2)+(51*x^2+8*x-1+14*x^3-336*x^5+110*x^4-744*x^6) *hypergeom([5/4, 7/4],[2],64*x^3*(1+x)/(1-4*x^2)^2))/((1-4*x^2)^(7/2)*(1+x)^2*(1-9*x)^2),x))/(1-2*x-15*x^2)^(5/2),x),x),x)/x^3. - 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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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: A114624 A091024 A275289 * A083309 A318264 A164979
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved