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

Author

Jonathan Vos Post, Dec 16 2010

Keywords

• nonn
• walk

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

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

Crossrefs

Cf. A002894, A008855.

Formula

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