A151371 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), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0)}.

1, 0, 2, 4, 16, 64, 266, 1210, 5630, 27338, 136182, 695270, 3622134, 19202912, 103375978, 564014502, 3114100008, 17377324802, 97897946434, 556290574936, 3185821992528, 18375238184570, 106677854854822, 623039452424644, 3658928077976048, 21597785683494184, 128091748188993146, 763037745974345554

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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 55, Tag 56.

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

Crossrefs

Sequence in context: A092585 A106186 A155543 * A001900 A113247 A280132

Adjacent sequences: A151368 A151369 A151370 * A151372 A151373 A151374

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved