A312822 Coordination sequence Gal.6.577.1 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, 16, 22, 28, 34, 34, 42, 42, 52, 60, 66, 72, 78, 70, 86, 78, 96, 104, 110, 116, 122, 106, 130, 114, 140, 148, 154, 160, 166, 142, 174, 150, 184, 192, 198, 204, 210, 178, 218, 186, 228, 236, 242, 248, 254, 214, 262, 222

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 21 2021: (Start)

a(n) = 2*a(n-2) - 3*a(n-4) + 4*a(n-6) - 3*a(n-8) + 2*a(n-10) - a(n-12) for n > 13.

G.f.: (-2*x^13 + 3*x^12 + 6*x^11 + 4*x^10 + 6*x^9 + 11*x^8 + 10*x^7 + 10*x^6 + 8*x^5 + 9*x^4 + 8*x^3 + 6*x^2 + 4*x + 1)/((x - 1)^2*(x + 1)^2*(x^4 + 1)^2). (End)

Crossrefs

Sequence in context: A312819 A312820 A312821 * A340298 A053688 A036302

Adjacent sequences: A312819 A312820 A312821 * A312823 A312824 A312825

Keyword

nonn

Author

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

Status

approved