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A151305 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), (0, 1), (1, -1), (1, 0)} 0
1, 2, 8, 34, 158, 780, 3994, 21108, 114172, 629550, 3526532, 20018456, 114931060, 666344104, 3896536944, 22958243962, 136180482166, 812648207806, 4875775540560, 29397986052418, 178046737441226, 1082749224714626, 6609289796906656, 40484406966736922, 248779468243690200, 1533328518945579542 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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: A150899 A150900 A084207 * A150901 A046649 A174808

Adjacent sequences:  A151302 A151303 A151304 * A151306 A151307 A151308

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified June 26 21:14 EDT 2022. Contains 354885 sequences. (Running on oeis4.)