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A151329 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (0, 1), (1, -1), (1, 0), (1, 1)} 0
1, 3, 16, 86, 509, 3065, 19088, 120401, 771758, 4991255, 32580974, 214030883, 1414515215, 9392000723, 62625868280, 419056150250, 2812961273801, 18933686864261, 127752378798614, 863851325189957, 5852685174009545, 39721858765234379, 270018313988209400, 1838154015475958213 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

A. Bostan, Computer Algebra for Lattice Path Combinatorics, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.

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

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

FORMULA

G.f. Int(1+Int((2*x+1)*(5*x+1)*(10+Int(12*(1-2*x-35*x^2)^(3/2)*((1+12*x^2)*(736*x^5+2208*x^4+1096*x^3-44*x^2+44*x+1)*hypergeom([7/4, 9/4],[2],64*(x^2+x+1)*x^2/(1+12*x^2)^2)-7*x*(1824*x^6+2496*x^5+1288*x^4+452*x^3+420*x^2+53*x+10)*hypergeom([9/4, 11/4],[3],64*(x^2+x+1)*x^2/(1+12*x^2)^2))/((5*x+1)*(1+12*x^2)^(9/2)*(2*x+1)^2),x))/(1-2*x-35*x^2)^(5/2),x),x)/((2*x+1)*x).   Mark van Hoeij, Aug 16 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[-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] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

CROSSREFS

Sequence in context: A278681 A224869 A163604 * A026111 A026330 A146963

Adjacent sequences:  A151326 A151327 A151328 * A151330 A151331 A151332

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 20 01:13 EDT 2018. Contains 316378 sequences. (Running on oeis4.)