A315317 Coordination sequence Gal.5.257.3 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, 10, 16, 21, 25, 32, 37, 41, 48, 52, 56, 64, 68, 72, 80, 83, 87, 96, 99, 103, 112, 114, 118, 128, 130, 134, 144, 145, 149, 160, 161, 165, 176, 176, 180, 192, 192, 196, 208, 207, 211, 224, 223, 227, 240, 238, 242, 256, 254

Offset

0,2

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

Table of n, a(n) for n=0..49.

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

Formula

Conjectures from Chai Wah Wu, Oct 19 2020: (Start)

a(n) = a(n-1) - a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) + a(n-7) - a(n-8) for n > 8.

G.f.: (x^8 + 5*x^7 + 5*x^6 + 10*x^5 + 5*x^4 + 10*x^3 + 5*x^2 + 5*x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)^2). (End)

Crossrefs

Sequence in context: A315314 A315315 A315316 * A315318 A315319 A315320

Adjacent sequences: A315314 A315315 A315316 * A315318 A315319 A315320

Keyword

nonn

Author

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

Status

approved