A311042 Coordination sequence Gal.4.11.4 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, 11, 14, 19, 23, 27, 31, 33, 36, 42, 46, 50, 54, 55, 58, 65, 69, 73, 77, 77, 80, 88, 92, 96, 100, 99, 102, 111, 115, 119, 123, 121, 124, 134, 138, 142, 146, 143, 146, 157, 161, 165, 169, 165, 168, 180, 184, 188

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

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

Crossrefs

Sequence in context: A303750 A160592 A311041 * A311043 A311044 A311045

Adjacent sequences: A311039 A311040 A311041 * A311043 A311044 A311045

Keyword

nonn

Author

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

Status

approved