A310218 Coordination sequence Gal.5.20.2 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, 3, 7, 12, 14, 21, 25, 26, 29, 35, 40, 40, 49, 53, 52, 55, 63, 68, 66, 77, 81, 78, 81, 91, 96, 92, 105, 109, 104, 107, 119, 124, 118, 133, 137, 130, 133, 147, 152, 144, 161, 165, 156, 159, 175, 180, 170, 189, 193, 182

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 27 2022: (Start)

a(n) = 2*a(n-7) - a(n-14) for n > 14.

G.f.: (x^14 + 3*x^13 + 7*x^12 + 12*x^11 + 16*x^10 + 21*x^9 + 23*x^8 + 24*x^7 + 25*x^6 + 21*x^5 + 14*x^4 + 12*x^3 + 7*x^2 + 3*x + 1)/(x^14 - 2*x^7 + 1). (End)

Crossrefs

Sequence in context: A310216 A310217 A187481 * A295423 A339583 A346867

Adjacent sequences: A310215 A310216 A310217 * A310219 A310220 A310221

Keyword

nonn

Author

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

Status

approved