A313217 Coordination sequence Gal.6.382.4 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, 4, 9, 15, 19, 25, 32, 35, 40, 46, 50, 54, 62, 67, 69, 76, 81, 84, 91, 99, 101, 104, 112, 115, 119, 128, 134, 135, 140, 148, 150, 155, 164, 168, 169, 176, 184, 185, 191, 200, 202, 204, 213, 219, 219, 227, 235, 236, 241, 250

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, Jun 06 2024: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 5*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 4*a(n-10) + 5*a(n-11) - 5*a(n-12) + 4*a(n-13) - 3*a(n-14) + 2*a(n-15) - a(n-16) for n > 19.

G.f.: (-x^19 + x^18 - x^17 + 2*x^16 + x^15 + 6*x^14 + 2*x^13 + 10*x^12 + 6*x^11 + 13*x^10 + 9*x^9 + 10*x^8 + 12*x^7 + 8*x^6 + 11*x^5 + 5*x^4 + 5*x^3 + 4*x^2 + 2*x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A313216 A189388 A184916 * A313218 A313219 A184931

Adjacent sequences: A313214 A313215 A313216 * A313218 A313219 A313220

Keyword

nonn

Author

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

Status

approved