A315907 Coordination sequence Gal.3.40.3 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

1, 6, 8, 14, 20, 22, 28, 34, 36, 42, 48, 50, 56, 62, 64, 70, 76, 78, 84, 90, 92, 98, 104, 106, 112, 118, 120, 126, 132, 134, 140, 146, 148, 154, 160, 162, 168, 174, 176, 182, 188, 190, 196, 202, 204, 210, 216, 218, 224, 230

Offset: 0

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

• nonn

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

• Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers.

Crossrefs

Cf. A047342.

Formula

Conjectures from R. J. Mathar, May 02 2023: (Start)

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

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.

a(n) = 2*A047342(n+1) for n > 0. (End)