A313153 Coordination sequence Gal.5.113.2 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, 4, 9, 14, 20, 26, 32, 37, 42, 46, 50, 55, 60, 66, 72, 78, 83, 88, 92, 96, 101, 106, 112, 118, 124, 129, 134, 138, 142, 147, 152, 158, 164, 170, 175, 180, 184, 188, 193, 198, 204, 210, 216, 221, 226, 230, 234, 239, 244, 250

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, May 08 2025: (Start)

a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.

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

Conjecture: a(n) ~ 46*n/9. - Stefano Spezia, May 09 2025

Crossrefs

Sequence in context: A313150 A313151 A313152 * A313154 A313155 A347581

Adjacent sequences: A313150 A313151 A313152 * A313154 A313155 A313156

Keyword

nonn

Author

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

Status

approved