A151315 - OEIS

A151315

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)}

1, 3, 10, 37, 138, 526, 2030, 7877, 30782, 120726, 475008, 1874068, 7407446, 29329716, 116285466, 461555291, 1833766116, 7291280658, 29011041208, 115498923044, 460056287616, 1833313414216, 7308504710010, 29145182257596, 116260990142440, 463889711899484, 1851384051250070, 7390399587090530

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

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, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

CROSSREFS

Sequence in context: A296000 A360586 A242725 * A164048 A180717 A151049

Adjacent sequences: A151312 A151313 A151314 * A151316 A151317 A151318

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved