A313097 Coordination sequence Gal.5.195.1 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, 4, 9, 14, 19, 23, 28, 31, 39, 39, 49, 48, 58, 59, 65, 68, 75, 77, 88, 82, 97, 91, 107, 105, 112, 113, 121, 122, 137, 126, 146, 134, 155, 150, 159, 159, 168, 167, 185, 169, 195, 178, 204, 195, 205, 204, 215, 213, 234, 212

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, May 31 2026: (Start)

a(n) = - a(n-1) - a(n-3) - a(n-4) + 2*a(n-5) + 2*a(n-6) + 2*a(n-8) + 2*a(n-9) - a(n-10) - a(n-11) - a(n-13) - a(n-14) for n > 14.

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

Crossrefs

Sequence in context: A313094 A313095 A313096 * A313098 A313099 A313100

Adjacent sequences: A313094 A313095 A313096 * A313098 A313099 A313100

Keyword

nonn

Author

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

Status

approved