A315615 Coordination sequence Gal.6.609.6 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, 6, 12, 15, 18, 21, 24, 33, 42, 45, 48, 51, 54, 57, 60, 72, 84, 84, 84, 87, 90, 93, 96, 111, 126, 123, 120, 123, 126, 129, 132, 150, 168, 162, 156, 159, 162, 165, 168, 189, 210, 201, 192, 195, 198, 201, 204, 228, 252, 240

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

From Chai Wah Wu, Dec 20 2019: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 7*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 14 (conjectured).

G.f.: (x^14 + 4*x^13 + 3*x^12 + 5*x^11 + 5*x^10 + 6*x^9 + 7*x^8 + 13*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 5*x^3 + 3*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2) (conjectured). (End)

Crossrefs

Sequence in context: A141698 A306711 A290965 * A315616 A091011 A324771

Adjacent sequences: A315612 A315613 A315614 * A315616 A315617 A315618

Keyword

nonn

Author

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

Status

approved