A313730 Coordination sequence Gal.6.234.4 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, 10, 15, 20, 25, 29, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 137, 142, 147, 152, 157, 162, 167, 172, 177, 182, 187, 191, 196, 201, 206, 211, 216, 221, 226, 231, 236, 241

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, Aug 18 2025: (Start)

a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.

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

Crossrefs

Sequence in context: A382415 A313729 A367085 * A313731 A313732 A381337

Adjacent sequences: A313727 A313728 A313729 * A313731 A313732 A313733

Keyword

nonn

Author

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

Status

approved