A315605 Coordination sequence Gal.6.577.6 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, 14, 20, 24, 30, 38, 44, 50, 56, 52, 64, 60, 74, 82, 88, 94, 100, 88, 108, 96, 118, 126, 132, 138, 144, 124, 152, 132, 162, 170, 176, 182, 188, 160, 196, 168, 206, 214, 220, 226, 232, 196, 240, 204, 250, 258, 264, 270

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, Jan 12 2021: (Start)

a(n) = 2*a(n-2) - 3*a(n-4) + 4*a(n-6) - 3*a(n-8) + 2*a(n-10) - a(n-12) for n > 15.

G.f.: (-2*x^15 + 4*x^13 + x^12 + 12*x^10 + 8*x^9 - x^8 + 8*x^7 + 22*x^6 + 14*x^5 - x^4 + 2*x^3 + 10*x^2 + 6*x + 1)/((x - 1)^2*(x + 1)^2*(x^4 + 1)^2). (End)

Crossrefs

Sequence in context: A318145 A318262 A315604 * A315606 A315607 A315608

Adjacent sequences: A315602 A315603 A315604 * A315606 A315607 A315608

Keyword

nonn

Author

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

Status

approved