A315691 Coordination sequence Gal.5.306.5 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, 17, 22, 28, 34, 39, 44, 50, 56, 62, 68, 73, 78, 84, 90, 95, 100, 106, 112, 118, 124, 129, 134, 140, 146, 151, 156, 162, 168, 174, 180, 185, 190, 196, 202, 207, 212, 218, 224, 230, 236, 241, 246, 252, 258, 263, 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, Jan 25 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 + 3*x^7 + 2*x^6 + 4*x^5 + 2*x^4 + 3*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: A212449 A315689 A315690 * A315692 A315693 A315694

Adjacent sequences: A315688 A315689 A315690 * A315692 A315693 A315694

Keyword

nonn

Author

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

Status

approved