A314070 Coordination sequence Gal.6.657.2 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, 5, 11, 15, 22, 27, 31, 38, 42, 48, 54, 58, 65, 69, 74, 81, 85, 91, 96, 101, 107, 111, 118, 123, 127, 134, 138, 144, 150, 154, 161, 165, 170, 177, 181, 187, 192, 197, 203, 207, 214, 219, 223, 230, 234, 240, 246, 250, 257, 261

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 02 2023: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 3*a(n-3) - 4*a(n-4) + 4*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 3*a(n-9) - 2*a(n-10) + 2*a(n-11) - a(n-12) for n > 12.

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

Crossrefs

Sequence in context: A314067 A314068 A314069 * A314071 A314072 A314073

Adjacent sequences: A314067 A314068 A314069 * A314071 A314072 A314073

Keyword

nonn

Author

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

Status

approved