A311285 Coordination sequence Gal.4.70.2 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, 12, 16, 21, 26, 30, 34, 37, 40, 45, 50, 55, 60, 63, 66, 70, 74, 79, 84, 88, 92, 96, 100, 104, 108, 112, 116, 121, 126, 130, 134, 137, 140, 145, 150, 155, 160, 163, 166, 170, 174, 179, 184, 188, 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, Feb 28 2022: (Start)

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

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

Crossrefs

Sequence in context: A311282 A311283 A311284 * A311286 A311287 A311288

Adjacent sequences: A311282 A311283 A311284 * A311286 A311287 A311288

Keyword

nonn

Author

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

Status

approved