A313025 Coordination sequence Gal.5.65.5 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, 4, 9, 14, 18, 22, 26, 30, 35, 40, 44, 48, 53, 58, 62, 66, 70, 74, 79, 84, 88, 92, 97, 102, 106, 110, 114, 118, 123, 128, 132, 136, 141, 146, 150, 154, 158, 162, 167, 172, 176, 180, 185, 190, 194, 198, 202, 206, 211, 216

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 10 2020: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - a(n-10) for n > 10.

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

Crossrefs

Sequence in context: A141089 A313023 A313024 * A313026 A313027 A313028

Adjacent sequences: A313022 A313023 A313024 * A313026 A313027 A313028

Keyword

nonn

Author

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

Status

approved