A313896 Coordination sequence Gal.6.364.4 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, 10, 16, 21, 27, 33, 37, 42, 48, 54, 59, 63, 69, 75, 80, 86, 91, 96, 101, 106, 112, 117, 123, 129, 133, 138, 144, 150, 155, 159, 165, 171, 176, 182, 187, 192, 197, 202, 208, 213, 219, 225, 229, 234, 240, 246, 251, 255, 261

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, Jan 12 2023: (Start)

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

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

Crossrefs

Sequence in context: A277645 A075003 A313895 * A313897 A313898 A313899

Adjacent sequences: A313893 A313894 A313895 * A313897 A313898 A313899

Keyword

nonn

Author

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

Status

approved