A151316 - OEIS

A151316

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, 0), (0, 1), (1, 0), (1, 1)}

1, 3, 12, 51, 225, 1020, 4691, 21859, 102708, 486132, 2313507, 11061139, 53085223, 255590813, 1233990233, 5971857421, 28960718794, 140702481744, 684696284001, 3336735766754, 16282068484389, 79543793479479, 389013643164321, 1904338699220063, 9330579503155732, 45753751710340198, 224528126328635579

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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.

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, 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: A166482 A007854 A151182 * A151183 A180898 A110167

Adjacent sequences: A151313 A151314 A151315 * A151317 A151318 A151319

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved