A314829 Coordination sequence Gal.4.41.3 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, 5, 9, 14, 18, 22, 27, 31, 36, 41, 45, 50, 54, 58, 63, 67, 72, 77, 81, 86, 90, 94, 99, 103, 108, 113, 117, 122, 126, 130, 135, 139, 144, 149, 153, 158, 162, 166, 171, 175, 180, 185, 189, 194, 198, 202, 207, 211, 216, 221

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 08 2022: (Start)

a(n) = 2*a(n-1) - a(n-2) - a(n-4) + 2*a(n-5) - a(n-6) for n > 6.

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

Crossrefs

Sequence in context: A314827 A314828 A299405 * A287243 A314830 A314831

Adjacent sequences: A314826 A314827 A314828 * A314830 A314831 A314832

Keyword

nonn

Author

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

Status

approved