A312969 Coordination sequence Gal.6.254.3 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, 9, 13, 19, 23, 27, 31, 35, 41, 45, 50, 54, 58, 63, 67, 73, 77, 81, 85, 89, 95, 99, 104, 108, 112, 117, 121, 127, 131, 135, 139, 143, 149, 153, 158, 162, 166, 171, 175, 181, 185, 189, 193, 197, 203, 207, 212, 216, 220

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 14 2020: (Start)

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

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

Crossrefs

Sequence in context: A312966 A312967 A312968 * A312970 A312971 A312972

Adjacent sequences: A312966 A312967 A312968 * A312970 A312971 A312972

Keyword

nonn

Author

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

Status

approved