A310999 Coordination sequence Gal.4.7.3 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, 8, 10, 15, 20, 23, 30, 32, 34, 40, 44, 50, 52, 55, 60, 63, 70, 72, 74, 80, 84, 90, 92, 95, 100, 103, 110, 112, 114, 120, 124, 130, 132, 135, 140, 143, 150, 152, 154, 160, 164, 170, 172, 175, 180, 183, 190, 192, 194

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) = 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 > 13.

G.f.: (-2*x^13 + 2*x^12 + x^10 + 4*x^9 - 2*x^8 + 4*x^7 + 3*x^6 + 5*x^4 + 2*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: A153975 A334834 A020169 * A311000 A302338 A311001

Adjacent sequences: A310996 A310997 A310998 * A311000 A311001 A311002

Keyword

nonn

Author

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

Status

approved