A315316 Coordination sequence Gal.6.324.5 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, 31, 35, 40, 46, 50, 56, 62, 66, 72, 77, 81, 87, 91, 96, 102, 106, 112, 118, 122, 128, 133, 137, 143, 147, 152, 158, 162, 168, 174, 178, 184, 189, 193, 199, 203, 208, 214, 218, 224, 230, 234, 240, 245, 249

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 12 2025: (Start)

a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.

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

Conjecture: a(n) ~ 56*n/11. - Stefano Spezia, Jun 12 2025

Crossrefs

Sequence in context: A336762 A315314 A315315 * A315317 A315318 A315319

Adjacent sequences: A315313 A315314 A315315 * A315317 A315318 A315319

Keyword

nonn

Author

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

Status

approved