A178106 Number of closed walks of length 16 and algebraic area n in the square lattice.

33820044, 28133728, 18569808, 10127744, 5015108, 2289760, 1036368, 435040, 184104, 73056, 28064, 10336, 3760, 1088, 352, 96, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Comments

n=16 column of Table 1.1, p.9, Mohammad-Noori. Histogram of the number of closed walks for n = 16, 32, 64.

The algebraic area is a signed quantity, and can become zero for self-intersecting paths.

Links

Table of n, a(n) for n=0..31.

Morteza Mohammad-Noori, Enumeration of closed random walks in the square lattice according to their areas, arXiv:1012.3720, Dec 16, 2010.

Formula

a(0) + 2*Sum_{n>0} a(n) = A002894(8).

Crossrefs

Cf. A002894, A008855.

Sequence in context: A246108 A184984 A143511 * A205943 A232636 A345121

Adjacent sequences: A178103 A178104 A178105 * A178107 A178108 A178109

Keyword

nonn,walk

Author

Jonathan Vos Post, Dec 16 2010

Status

approved