A315418 Coordination sequence Gal.3.21.3 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, 11, 15, 20, 26, 32, 37, 41, 46, 52, 58, 63, 67, 72, 78, 84, 89, 93, 98, 104, 110, 115, 119, 124, 130, 136, 141, 145, 150, 156, 162, 167, 171, 176, 182, 188, 193, 197, 202, 208, 214, 219, 223, 228, 234, 240, 245, 249, 254

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, Jul 10 2025: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

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

Conjecture: a(n) ~ 26*n/5. - Stefano Spezia, Jul 11 2025

Crossrefs

Sequence in context: A315415 A315416 A315417 * A315419 A315420 A315421

Adjacent sequences: A315415 A315416 A315417 * A315419 A315420 A315421

Keyword

nonn

Author

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

Status

approved