A313059 Coordination sequence Gal.4.99.1 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, 18, 23, 29, 32, 37, 44, 45, 50, 59, 59, 64, 74, 72, 77, 89, 86, 91, 104, 99, 104, 119, 113, 118, 134, 126, 131, 149, 140, 145, 164, 153, 158, 179, 167, 172, 194, 180, 185, 209, 194, 199, 224, 207, 212, 239, 221

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 28 2020: (Start)

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

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

Crossrefs

Sequence in context: A313056 A313057 A313058 * A313060 A313061 A313062

Adjacent sequences: A313056 A313057 A313058 * A313060 A313061 A313062

Keyword

nonn

Author

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

Status

approved