A312860 Coordination sequence Gal.6.546.6 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, 4, 9, 12, 17, 21, 25, 30, 32, 38, 43, 44, 51, 55, 59, 64, 64, 72, 77, 76, 85, 89, 93, 98, 96, 106, 111, 108, 119, 123, 127, 132, 128, 140, 145, 140, 153, 157, 161, 166, 160, 174, 179, 172, 187, 191, 195, 200, 192, 208

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, May 15 2026: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) + a(n-8) - a(n-9) + a(n-10) - a(n-11) + a(n-12) - a(n-13) + a(n-14) - a(n-15) for n > 15.

G.f.: (x^15 + 3*x^14 + 6*x^13 + 7*x^12 + 10*x^11 + 10*x^10 + 15*x^9 + 15*x^8 + 15*x^7 + 15*x^6 + 10*x^5 + 11*x^4 + 6*x^3 + 6*x^2 + 3*x + 1)/((x - 1)^2*(x + 1)*(x^2 + 1)^2*(x^4 + 1)^2). (End)

Crossrefs

Sequence in context: A047461 A276873 A190448 * A312861 A301688 A276885

Adjacent sequences: A312857 A312858 A312859 * A312861 A312862 A312863

Keyword

nonn

Author

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

Status

approved