A151350 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, 1)}.

1, 0, 1, 1, 6, 17, 58, 202, 749, 2901, 11318, 45171, 183265, 756196, 3159230, 13341971, 56903856, 244855696, 1061995972, 4638725316, 20391632508, 90164737708, 400807229526, 1790417941480, 8033839546376, 36198663913941, 163730600062179, 743218114133634, 3384894808811735, 15463955571145905

Offset

0,5

Links

Table of n, a(n) for n=0..29.

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 30

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, 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: A088016 A010330 A109311 * A195741 A006758 A363165

Adjacent sequences: A151347 A151348 A151349 * A151351 A151352 A151353

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved