Coordination sequence Gal.3.47.3 where GGal.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.

OEIS Server: https://oeis.org/edit/global/2973

reviewed

approved

proposed

reviewed

editing

proposed

Conjectures from Chai Wah Wu, Aug 03 2020: (Start)

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

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

approved

editing

0,2

Brian GalebacheGalebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>

OEIS Server: https://oeis.org/edit/global/2762

Coordination sequence Gal.3.47.3 where G.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, 6, 9, 11, 14, 19, 26, 31, 32, 33, 37, 44, 52, 56, 55, 55, 60, 69, 78, 81, 78, 77, 83, 94, 104, 106, 101, 99, 106, 119, 130, 131, 124, 121, 129, 144, 156, 156, 147, 143, 152, 169, 182, 181, 170, 165, 175, 194, 208, 206

0

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.

Brian Galebache, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>

nonn

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

approved