A313145 Coordination sequence Gal.6.264.1 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, 4, 9, 14, 20, 25, 29, 33, 38, 44, 49, 54, 58, 62, 67, 72, 78, 83, 87, 91, 96, 102, 107, 112, 116, 120, 125, 130, 136, 141, 145, 149, 154, 160, 165, 170, 174, 178, 183, 188, 194, 199, 203, 207, 212, 218, 223, 228, 232, 236

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, Jun 02 2025: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - a(n-12) for n > 12.

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

Conjecture: a(n) ~ 29*n/6. - Stefano Spezia, Jun 05 2025

Crossrefs

Sequence in context: A313142 A313143 A313144 * A313146 A313147 A184515

Adjacent sequences: A313142 A313143 A313144 * A313146 A313147 A313148

Keyword

nonn

Author

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

Status

approved