A151353 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, -1), (-1, 0), (0, -1), (1, 1)}.

1, 0, 1, 2, 2, 14, 21, 76, 252, 566, 2282, 6248, 19958, 69356, 205129, 720868, 2340178, 7692570, 26681224, 87814024, 302838250, 1035805496, 3526054994, 12286338876, 42255768876, 147090631152, 513835481206, 1790785075144, 6298459417432, 22120204885156, 77965202090697, 275780508039312, 975587671958542

Offset

0,4

Links

Table of n, a(n) for n=0..32.

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 5, Tag 16.

M. Bousquet-Mélou and M. Mishna, Walks with small steps in the quarter plane, arXiv:0810.4387 [math.CO], 2008-2009.

Igor Pak, Complexity problems in enumerative combinatorics, arXiv:1803.06636 [math.CO], 2018.

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

Crossrefs

Sequence in context: A032134 A032038 A187734 * A151437 A235349 A226157

Adjacent sequences: A151350 A151351 A151352 * A151354 A151355 A151356

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved