A310102 Coordination sequence Gal.4.16.1 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, 3, 6, 11, 16, 18, 21, 24, 27, 30, 38, 43, 42, 45, 48, 51, 54, 65, 70, 66, 69, 72, 75, 78, 92, 97, 90, 93, 96, 99, 102, 119, 124, 114, 117, 120, 123, 126, 146, 151, 138, 141, 144, 147, 150, 173, 178, 162, 165, 168

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, Dec 24 2019: (Start)

a(n) = 2*a(n-7) - a(n-14) for n > 14.

G.f.: (x^14 + 3*x^13 + 6*x^12 + 11*x^11 + 16*x^10 + 18*x^9 + 21*x^8 + 22*x^7 + 21*x^6 + 18*x^5 + 16*x^4 + 11*x^3 + 6*x^2 + 3*x + 1)/(x^14 - 2*x^7 + 1). (End)

Crossrefs

Sequence in context: A363652 A368586 A310101 * A310103 A310104 A310105

Adjacent sequences: A310099 A310100 A310101 * A310103 A310104 A310105

Keyword

nonn

Author

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

Status

approved