A315303 Coordination sequence Gal.6.247.6 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, 20, 24, 28, 32, 38, 42, 48, 54, 58, 64, 68, 72, 76, 80, 86, 90, 96, 102, 106, 112, 116, 120, 124, 128, 134, 138, 144, 150, 154, 160, 164, 168, 172, 176, 182, 186, 192, 198, 202, 208, 212, 216, 220, 224, 230, 234

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, Apr 15 2025: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - a(n-10) for n > 10.

G.f.: (x^10 + 4*x^9 + 6*x^7 - 2*x^6 + 6*x^5 - 2*x^4 + 6*x^3 + 4*x + 1)/((x - 1)^2*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A315300 A315301 A315302 * A315304 A315305 A315306

Adjacent sequences: A315300 A315301 A315302 * A315304 A315305 A315306

Keyword

nonn

Author

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

Status

approved