A313940 Coordination sequence Gal.4.138.2 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, 10, 16, 23, 29, 34, 38, 45, 52, 57, 60, 64, 73, 81, 86, 88, 93, 102, 109, 112, 114, 121, 131, 138, 140, 143, 150, 159, 164, 166, 171, 179, 188, 192, 195, 200, 207, 214, 218, 223, 229, 236, 242, 247, 252, 257, 262, 268, 275

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, Apr 19 2024: (Start)

a(n) = a(n-1) - a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + a(n-7) + a(n-8) - a(n-9) + a(n-11) - a(n-12) for n > 12.

G.f.: (x + 1)^2*(x^10 + 2*x^9 + 5*x^7 + x^6 + 3*x^5 + x^4 + 5*x^3 + 2*x + 1)/((x - 1)^2*(x^6 + x^3 + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A313937 A313938 A313939 * A212455 A052905 A365701

Adjacent sequences: A313937 A313938 A313939 * A313941 A313942 A313943

Keyword

nonn,changed

Author

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

Status

approved