A312933 Coordination sequence Gal.6.131.3 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, 18, 22, 27, 32, 36, 41, 45, 50, 54, 58, 63, 67, 72, 76, 81, 86, 90, 95, 99, 104, 108, 112, 117, 121, 126, 130, 135, 140, 144, 149, 153, 158, 162, 166, 171, 175, 180, 184, 189, 194, 198, 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) = 2*a(n-1) - a(n-2) - a(n-6) + 2*a(n-7) - a(n-8) for n > 8.

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

Crossrefs

Sequence in context: A312931 A312932 A330183 * A206908 A330179 A312934

Adjacent sequences: A312930 A312931 A312932 * A312934 A312935 A312936

Keyword

nonn

Author

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

Status

approved