A312210 Coordination sequence Gal.6.159.1 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, 13, 19, 25, 31, 37, 43, 49, 54, 58, 62, 66, 70, 75, 81, 87, 93, 99, 105, 111, 116, 120, 124, 128, 132, 137, 143, 149, 155, 161, 167, 173, 178, 182, 186, 190, 194, 199, 205, 211, 217, 223, 229, 235, 240, 244, 248, 252

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, Aug 01 2021: (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) - 2*a(n-10) + 2*a(n-11) - a(n-12) for n > 12.

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

Crossrefs

Sequence in context: A312207 A312208 A312209 * A312211 A034856 A365700

Adjacent sequences: A312207 A312208 A312209 * A312211 A312212 A312213

Keyword

nonn

Author

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

Status

approved