A314054 Coordination sequence Gal.4.142.2 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, 11, 15, 21, 26, 32, 38, 43, 49, 53, 59, 64, 69, 75, 79, 85, 90, 96, 102, 107, 113, 117, 123, 128, 133, 139, 143, 149, 154, 160, 166, 171, 177, 181, 187, 192, 197, 203, 207, 213, 218, 224, 230, 235, 241, 245, 251, 256, 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, Jan 25 2020: (Start)

a(n) = 2*a(n-1) - a(n-2) - a(n-4) + 2*a(n-5) - a(n-6) - a(n-8) + 2*a(n-9) - a(n-10) for n > 10.

G.f.: (x^10 + 3*x^9 + 2*x^8 - 2*x^7 + 3*x^6 + 2*x^5 + 3*x^4 - 2*x^3 + 2*x^2 + 3*x + 1)/(x^8*(x - 1)^2 + x^4*(x - 1)^2 + (x - 1)^2). (End)

Crossrefs

Sequence in context: A314051 A314052 A314053 * A314055 A284621 A314056

Adjacent sequences: A314051 A314052 A314053 * A314055 A314056 A314057

Keyword

nonn

Author

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

Status

approved