A310215 Coordination sequence Gal.3.2.1 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, 17, 22, 27, 28, 31, 37, 42, 42, 45, 52, 57, 56, 59, 67, 72, 70, 73, 82, 87, 84, 87, 97, 102, 98, 101, 112, 117, 112, 115, 127, 132, 126, 129, 142, 147, 140, 143, 157, 162, 154, 157, 172, 177, 168, 171

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, Sep 24 2020: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4) - a(n-5) + a(n-6) - a(n-7) for n > 7.

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

Crossrefs

Sequence in context: A270122 A142958 A310214 * A310216 A310217 A187481

Adjacent sequences: A310212 A310213 A310214 * A310216 A310217 A310218

Keyword

nonn

Author

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

Status

approved