A315203 Coordination sequence Gal.6.321.6 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, 14, 20, 24, 28, 34, 38, 42, 48, 54, 58, 62, 68, 72, 76, 82, 86, 90, 96, 102, 106, 110, 116, 120, 124, 130, 134, 138, 144, 150, 154, 158, 164, 168, 172, 178, 182, 186, 192, 198, 202, 206, 212, 216, 220, 226, 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, Jun 19 2020: (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 + 4*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 4*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: A315201 A341693 A315202 * A315204 A315205 A315206

Adjacent sequences: A315200 A315201 A315202 * A315204 A315205 A315206

Keyword

nonn

Author

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

Status

approved