A313295 Coordination sequence Gal.5.90.1 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, 9, 15, 21, 27, 33, 39, 45, 50, 54, 58, 63, 69, 75, 81, 87, 93, 99, 104, 108, 112, 117, 123, 129, 135, 141, 147, 153, 158, 162, 166, 171, 177, 183, 189, 195, 201, 207, 212, 216, 220, 225, 231, 237, 243, 249, 255, 261, 266

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 30 2024: (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) - a(n-10) for n > 10.

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

Crossrefs

Sequence in context: A313292 A313293 A313294 * A313296 A313297 A270545

Adjacent sequences: A313292 A313293 A313294 * A313296 A313297 A313298

Keyword

nonn

Author

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

Status

approved