A151361 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, 0), (1, 1)}.

1, 2, 13, 124, 1427, 18424, 257090, 3794091, 58411957, 929535968, 15190791558, 253735278108, 4316305707838, 74571507312612, 1305616160300541, 23124883139330156, 413757060245969804, 7469673227755295934, 135931742489359394834, 2491396081566293784574, 45957915237430642944461

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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 27, Tag 32.

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[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, 2 n], {n, 0, 25}]

Crossrefs

Sequence in context: A004122 A359124 A086630 * A328008 A372103 A073559

Adjacent sequences: A151358 A151359 A151360 * A151362 A151363 A151364

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved