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A151347 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1)}. 2
1, 0, 1, 1, 3, 8, 19, 65, 177, 611, 1928, 6648, 22928, 80851, 292343, 1063611, 3957406, 14818681, 56339994, 215943994, 836246604, 3265240671, 12848804154, 50936668789, 203235590343, 816070826188, 3295317218038, 13379003847708, 54588942258042, 223782828113783, 921414594957514, 3809576782931810 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..500

A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 35, Tag 39.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Colin Defant, Motzkin Intervals and Valid Hook Configurations, arXiv:1904.10451 [math.CO], 2019.

Maya Sankar, Further Bijections to Pattern-Avoiding Valid Hook Configurations, arXiv:1910.08895 [math.CO], 2019.

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

CROSSREFS

Sequence in context: A018032 A086808 A170900 * A047093 A304256 A060305

Adjacent sequences:  A151344 A151345 A151346 * A151348 A151349 A151350

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 21 01:33 EST 2019. Contains 329349 sequences. (Running on oeis4.)