A310492 Coordination sequence Gal.6.249.6 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, 10, 16, 20, 24, 28, 32, 38, 44, 48, 52, 58, 64, 68, 72, 76, 80, 86, 92, 96, 100, 106, 112, 116, 120, 124, 128, 134, 140, 144, 148, 154, 160, 164, 168, 172, 176, 182, 188, 192, 196, 202, 208, 212, 216, 220, 224, 230, 236

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, Jan 05 2024: (Start)

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

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

Crossrefs

Sequence in context: A310489 A310490 A310491 * A310493 A310494 A310495

Adjacent sequences: A310489 A310490 A310491 * A310493 A310494 A310495

Keyword

nonn

Author

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

Status

approved