OFFSET
0,3
LINKS
A. Bostan, Computer Algebra for Lattice Path Combinatorics, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.
Alin Bostan, Calcul Formel pour la Combinatoire des Marches [The text is in English], Habilitation à Diriger des Recherches, Laboratoire d’Informatique de Paris Nord, Université Paris 13, December 2017.
A. Bostan and M. Kauers, Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO], 2008-2009.
M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.
FORMULA
G.f.: Int(-1+Int((1+x)*(3*x+1)*Int(12*(1-2*x-15*x^2)^(3/2)*((8*x^2-1)*(2280*x^5+621*x^4-104*x^3-117*x^2-14*x+2)*hypergeom([7/4, 9/4],[2],64*(x^2+1)*x^2/(16*x^2+1)^2)-x*(280*x^6-297*x^5-562*x^4-406*x^3+128*x^2+11*x+10)*hypergeom([7/4, 9/4],[3],64*(x^2+1)*x^2/(16*x^2+1)^2))/((3*x+1)*(16*x^2+1)^(9/2)*(1+x)^2),x)/(1-2*x-15*x^2)^(5/2),x),x)/((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, 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
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved