A313912 Coordination sequence Gal.6.207.6 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, 16, 22, 27, 31, 35, 40, 46, 52, 57, 62, 67, 72, 78, 84, 89, 93, 97, 102, 108, 114, 119, 124, 129, 134, 140, 146, 151, 155, 159, 164, 170, 176, 181, 186, 191, 196, 202, 208, 213, 217, 221, 226, 232, 238, 243, 248, 253

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, Aug 08 2022: (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) - 2*a(n-10) + 2*a(n-11) - a(n-12) for n > 12.

G.f.: (x^12 + 3*x^11 + 2*x^10 + 4*x^9 + 2*x^8 + 3*x^7 + x^6 + 3*x^5 + 2*x^4 + 4*x^3 + 2*x^2 + 3*x + 1)/((x - 1)^2*(x^2 + 1)*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^2 + 1)). (End)

Crossrefs

Sequence in context: A313909 A313910 A313911 * A313913 A313914 A313915

Adjacent sequences: A313909 A313910 A313911 * A313913 A313914 A313915

Keyword

nonn

Author

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

Status

approved