A310100 Coordination sequence Gal.5.19.1 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, 15, 19, 23, 25, 28, 31, 34, 41, 45, 49, 53, 53, 56, 59, 62, 71, 75, 79, 83, 81, 84, 87, 90, 101, 105, 109, 113, 109, 112, 115, 118, 131, 135, 139, 143, 137, 140, 143, 146, 161, 165, 169, 173, 165, 168, 171

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.

Conjectures from Colin Barker, Apr 18 2020: (Start)

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

a(n) = a(n-1) - a(n-4) + a(n-5) + a(n-8) - a(n-9) + a(n-12) - a(n-13) for n>13.

(End)

Links

Table of n, a(n) for n=0..49.

Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers

Crossrefs

Sequence in context: A187896 A225521 A067278 * A234011 A368384 A113960

Adjacent sequences: A310097 A310098 A310099 * A310101 A310102 A310103

Keyword

nonn

Author

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

Extensions

Edited by Georg Fischer, Apr 17 2020

Status

approved