A315047 Coordination sequence Gal.5.204.4 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, 5, 9, 15, 20, 24, 28, 35, 39, 43, 50, 51, 59, 65, 66, 74, 76, 83, 89, 91, 98, 99, 109, 113, 114, 124, 122, 133, 139, 137, 148, 147, 157, 163, 162, 172, 170, 183, 187, 185, 198, 193, 207, 213, 208, 222, 218, 231, 237, 233

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 20 2025: (Start)

a(n) = - a(n-1) - a(n-2) + 2*a(n-5) + 2*a(n-6) + 2*a(n-7) - a(n-10) - a(n-11) - a(n-12) for n > 12.

G.f.: (x^2 + 1)^2*(x^8 + 6*x^7 + 13*x^6 + 17*x^5 + 17*x^4 + 17*x^3 + 13*x^2 + 6*x + 1)/((x - 1)^2*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)^2). (End)

Crossrefs

Sequence in context: A315044 A315045 A315046 * A315048 A315049 A315050

Adjacent sequences: A315044 A315045 A315046 * A315048 A315049 A315050

Keyword

nonn

Author

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

Status

approved