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A151476 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), (1, -1), (1, 0), (1, 1)} 0
1, 1, 4, 13, 52, 221, 969, 4476, 21050, 101708, 499482, 2491362, 12586523, 64275443, 331393163, 1722648256, 9020489609, 47541144560, 252014613424, 1342905834870, 7189725796882, 38658137171795, 208674158480442, 1130457902895656, 6144313389541112, 33497736351060064, 183139829758877682 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

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[-1 + i, 1 + 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[0, k, n], {k, 0, n}], {n, 0, 25}]

CROSSREFS

Sequence in context: A149464 A307398 A129147 * A140454 A149465 A149466

Adjacent sequences:  A151473 A151474 A151475 * A151477 A151478 A151479

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 29 15:44 EDT 2020. Contains 334704 sequences. (Running on oeis4.)