A311343 Coordination sequence Gal.4.60.1 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, 8, 12, 16, 22, 26, 30, 34, 36, 40, 46, 52, 56, 60, 62, 64, 70, 76, 82, 86, 88, 90, 94, 100, 106, 112, 114, 116, 120, 124, 130, 136, 140, 142, 146, 150, 154, 160, 164, 168, 172, 176, 180, 184, 188, 192, 198, 202, 206

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 03 2023: (Start)

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

G.f.: (x^12 + 3*x^11 + 5*x^10 + 7*x^9 + 9*x^8 + 13*x^7 + 12*x^6 + 13*x^5 + 9*x^4 + 7*x^3 + 5*x^2 + 3*x + 1)/(x^12 - x^11 + x^10 - x^9 + x^8 - x^7 - x^5 + x^4 - x^3 + x^2 - x + 1). (End)

Crossrefs

Sequence in context: A311340 A311341 A311342 * A311344 A311345 A311346

Adjacent sequences: A311340 A311341 A311342 * A311344 A311345 A311346

Keyword

nonn

Author

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

Status

approved