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

0,2

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).

Formula

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

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

Mathematica

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

Crossrefs

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

Sequence in context: A160998 A141205 A310237 * A310238 A299638 A189474

Adjacent sequences: A336702 A336703 A336704 * A336706 A336707 A336708

Keyword

nonn

Author

Sean A. Irvine, Jul 31 2020

Status

approved