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A151278
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), (0, 1), (1, 0)}.
1
1, 2, 4, 10, 26, 66, 178, 488, 1320, 3674, 10318, 28728, 81344, 231634, 655614, 1876510, 5391998, 15423550, 44473310, 128605264, 370583896, 1074340126, 3121406738, 9043275450, 26324579482, 76763009234, 223318464418, 652169185724, 1907256905140, 5566743069850, 16299205388766, 47779358006460
OFFSET
0,2
REFERENCES
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; https://specfun.inria.fr/bostan/HDR.pdf
LINKS
M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
A. Bostan, Computer Algebra for Lattice Path Combinatorics, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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[i, -1 + 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: A295704 A090032 A090377 * A307756 A149810 A095337
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved