A315850 Coordination sequence Gal.6.104.6 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, 8, 10, 12, 18, 26, 26, 28, 32, 34, 44, 46, 44, 52, 54, 60, 66, 62, 68, 74, 78, 84, 82, 86, 92, 96, 102, 100, 104, 112, 114, 120, 120, 120, 130, 134, 136, 140, 140, 146, 154, 154, 156, 160, 164, 172, 174, 174, 178

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 16 2025: (Start)

a(n) = a(n-3) - a(n-4) + a(n-5) + a(n-7) - a(n-8) + a(n-9) - a(n-12) for n > 12.

G.f.: (x^12 + 6*x^11 + 8*x^10 + 9*x^9 + 7*x^8 + 15*x^7 + 18*x^6 + 15*x^5 + 7*x^4 + 9*x^3 + 8*x^2 + 6*x + 1)/(x^12 - x^9 + x^8 - x^7 - x^5 + x^4 - x^3 + 1). (End)

Crossrefs

Sequence in context: A092121 A005525 A023385 * A315851 A348147 A168335

Adjacent sequences: A315847 A315848 A315849 * A315851 A315852 A315853

Keyword

nonn

Author

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

Status

approved