A315496 Coordination sequence Gal.5.306.3 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, 11, 16, 22, 28, 34, 40, 45, 50, 56, 62, 67, 72, 78, 84, 90, 96, 101, 106, 112, 118, 123, 128, 134, 140, 146, 152, 157, 162, 168, 174, 179, 184, 190, 196, 202, 208, 213, 218, 224, 230, 235, 240, 246, 252, 258, 264, 269, 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, Apr 05 2021: (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 + x^8 + 4*x^7 + 2*x^6 + 4*x^5 + 2*x^4 + 4*x^3 + 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: A315493 A315494 A315495 * A315497 A315498 A315499

Adjacent sequences: A315493 A315494 A315495 * A315497 A315498 A315499

Keyword

nonn

Author

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

Status

approved