A313962 Coordination sequence Gal.3.53.2 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, 5, 10, 17, 21, 27, 31, 38, 43, 48, 53, 58, 65, 69, 75, 79, 86, 91, 96, 101, 106, 113, 117, 123, 127, 134, 139, 144, 149, 154, 161, 165, 171, 175, 182, 187, 192, 197, 202, 209, 213, 219, 223, 230, 235, 240, 245, 250, 257, 261

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, Feb 02 2023: (Start)

a(n) = 2*a(n-1) - a(n-2) - a(n-3) + 2*a(n-4) - a(n-5) - a(n-6) + 2*a(n-7) - a(n-8) for n > 8.

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

Crossrefs

Sequence in context: A313959 A313960 A313961 * A313963 A313964 A313965

Adjacent sequences: A313959 A313960 A313961 * A313963 A313964 A313965

Keyword

nonn

Author

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

Status

approved