A310326 Coordination sequence Gal.4.23.1 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, 9, 15, 15, 21, 27, 30, 30, 42, 45, 45, 48, 60, 60, 60, 69, 78, 75, 78, 87, 93, 90, 99, 105, 108, 108, 117, 120, 123, 129, 135, 135, 141, 147, 150, 150, 162, 165, 165, 168, 180, 180, 180, 189, 198, 195, 198, 207, 213

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

G.f.: (1+3*x+9*x^2+15*x^3+14*x^4+18*x^5+18*x^6+14*x^7+12*x^8+12*x^9+3*x^10+x^11) / (1-x^4-x^7+x^11) = 1 + (30/7) / (1-x)^2 - (123/28) / (1-x) - (3/4) / (1+x) + (3/2)*x / (1+x^2) + (3/7) * (2-6*x-3*x^2+4*x^3+x^4-5*x^5) / (1+x+x^2+x^3+x^4+x^5+x^6). - Natalia L. Skirrow, Apr 20 2026

Prog

(Python)
A310326=lambda n: ( 10*n + (14*(0, 1, 0, -1)[n%4] - 1 - 7*(-1)**n)//4 + (2, -8, 3, 7, -3, -6, 5)[n%7] )*3//7 if n else 1 # Natalia L. Skirrow, Apr 20 2026

Crossrefs

Sequence in context: A366116 A385229 A310325 * A310327 A170841 A090158

Adjacent sequences: A310323 A310324 A310325 * A310327 A310328 A310329

Keyword

nonn

Author

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

Status

approved