A336742 -id:A336742 - cp's OEIS frontend

A336724 Number of n-step self-avoiding walks on the half-Manhattan square lattice.

1, 3, 7, 17, 37, 83, 181, 399, 863, 1887, 4057, 8797, 18851, 40649, 86911, 186705, 398413, 853407, 1818099, 3885377, 8266359, 17632961, 37473467, 79814011, 169457991, 360469139, 764700473, 1624915019, 3444615545, 7312733017, 15492242679, 32862908109, 69581860921, 147497088201

Offset: 0

Sean A. Irvine, Aug 01 2020

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

Sean A. Irvine, Java program (github)

Cf. A336705 (coordination sequence), A336742 (self-avoiding cycles), A117633 (Manhattan lattice), A001411 (square lattice), A322419 (L-lattice).

A336705 Coordination sequence for the half-Manhattan lattice.

Original entry on oeis.org

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

Sean A. Irvine, Jul 31 2020

nonn

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

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).

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

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

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

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

cp's OEIS Frontend

A336724 Number of n-step self-avoiding walks on the half-Manhattan square lattice.

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