A312402 Coordination sequence Gal.4.70.4 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, 8, 14, 18, 20, 24, 28, 32, 38, 44, 48, 50, 52, 56, 62, 68, 72, 76, 80, 82, 86, 92, 96, 100, 104, 108, 114, 118, 120, 124, 128, 132, 138, 144, 148, 150, 152, 156, 162, 168, 172, 176, 180, 182, 186, 192, 196, 200, 204

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, Dec 24 2019: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 6*a(n-6) + 6*a(n-7) - 5*a(n-8) + 4*a(n-9) - 3*a(n-10) + 2*a(n-11) - a(n-12) for n > 12.

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

Crossrefs

Sequence in context: A333465 A342274 A312401 * A312403 A312404 A312405

Adjacent sequences: A312399 A312400 A312401 * A312403 A312404 A312405

Keyword

nonn

Author

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

Status

approved