A315732 Coordination sequence Gal.6.640.6 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, 18, 22, 28, 34, 38, 44, 50, 56, 62, 68, 74, 78, 84, 90, 94, 100, 106, 112, 118, 124, 130, 134, 140, 146, 150, 156, 162, 168, 174, 180, 186, 190, 196, 202, 206, 212, 218, 224, 230, 236, 242, 246, 252, 258, 262, 268, 274

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 03 2020: (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) - a(n-10) for n > 10.

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

Crossrefs

Sequence in context: A315729 A315730 A315731 * A315733 A315734 A141515

Adjacent sequences: A315729 A315730 A315731 * A315733 A315734 A315735

Keyword

nonn

Author

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

Status

approved