A336705 Coordination sequence for the half-Manhattan lattice.

1, 3, 7, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228

Offset: 0

Author

Sean A. Irvine, Jul 31 2020

Keywords

• nonn

Comments

In the half-Manhattan lattice, E-W streets run alternately E and W, but N-S streets are two way.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Sean A. Irvine, Illustration of a(0) to a(7)
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A336627 (Manhattan lattice), A008574 (square lattice), A336726 (self-avoiding walks), A336742 (self-avoiding cycles).

Programs

Mathematica

LinearRecurrence[{2,-1},{1,3,7,12,16},100] (* Paolo Xausa, Sep 01 2023 *)

Formula

G.f.: (1+x) * (1+2*x^2-x^3) / (1-x)^2.

a(n) = 4*n, n >= 3.