A308409 Number of bond trees with n bonds on the square lattice.

1, 2, 6, 22, 87, 364, 1574, 6986, 31581, 144880, 672390, 3150362, 14877317, 70726936, 338158676

Offset: 0

Author

Douglas A. Torrance, May 25 2019

Keywords

• nonn
• more

Comments

a(n-1) is the number of bond trees with n sites (vertices) on the square lattice.

a(n) is the number of fixed polyedges (A096267) with n edges and no cycles.

Links

• D. S. Gaunt et al., Universality in branched polymers on d-dimensional hypercubic lattices, Journal of Physics A: Mathematical and General 15.10 (1982): 3209.
• Douglas A. Torrance, Enumeration of planar Tangles, arXiv:1906.01541 [math.CO], 2019. See Table 4.1 (A).
• S. G. Whittington, G. M. Torrie, and D. S. Gaunt, Branched polymers with a prescribed number of cycles, Journal of Physics A: Mathematical and General 16.8 (1983): 1695.