A315405 Coordination sequence Gal.3.15.3 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, 6, 11, 15, 19, 24, 30, 36, 41, 45, 49, 54, 60, 66, 71, 75, 79, 84, 90, 96, 101, 105, 109, 114, 120, 126, 131, 135, 139, 144, 150, 156, 161, 165, 169, 174, 180, 186, 191, 195, 199, 204, 210, 216, 221, 225, 229, 234, 240, 246

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, Sep 02 2025: (Start)

a(n) = 3*a(n-1) - 4*a(n-2) + 3*a(n-3) - a(n-4) for n > 4.

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

Crossrefs

Sequence in context: A315402 A315403 A315404 * A315406 A315407 A315408

Adjacent sequences: A315402 A315403 A315404 * A315406 A315407 A315408

Keyword

nonn

Author

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

Status

approved