A314772 Coordination sequence Gal.4.126.3 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, 13, 19, 26, 31, 35, 39, 45, 52, 57, 59, 63, 71, 78, 83, 83, 87, 97, 104, 109, 107, 111, 123, 130, 135, 131, 135, 149, 156, 161, 155, 159, 175, 182, 187, 179, 183, 201, 208, 213, 203, 207, 227, 234, 239, 227, 231, 253

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, Apr 15 2025: (Start)

a(n) = 2*a(n-5) - a(n-10) for n > 13.

G.f.: (-2*x^13 - 2*x^12 + x^10 + 7*x^9 + 13*x^8 + 17*x^7 + 21*x^6 + 24*x^5 + 19*x^4 + 13*x^3 + 9*x^2 + 5*x + 1)/(x^10 - 2*x^5 + 1). (End)

Crossrefs

Sequence in context: A314769 A314770 A314771 * A314773 A023493 A314774

Adjacent sequences: A314769 A314770 A314771 * A314773 A314774 A314775

Keyword

nonn

Author

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

Status

approved