A310683 Coordination sequence Gal.4.15.3 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, 7, 10, 13, 16, 22, 26, 27, 30, 33, 36, 44, 48, 47, 50, 53, 56, 66, 70, 67, 70, 73, 76, 88, 92, 87, 90, 93, 96, 110, 114, 107, 110, 113, 116, 132, 136, 127, 130, 133, 136, 154, 158, 147, 150, 153, 156, 176, 180

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 + 4*x^9 + 6*x^8 + 7*x^7 + 11*x^6 + 9*x^5 + 7*x^4 + 6*x^3 + 4*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: A090852 A182112 A090955 * A134027 A143455 A310684

Adjacent sequences: A310680 A310681 A310682 * A310684 A310685 A310686

Keyword

nonn

Author

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

Status

approved