A314697 Coordination sequence Gal.5.125.4 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, 5, 9, 13, 17, 24, 27, 34, 35, 44, 45, 52, 53, 62, 65, 70, 71, 80, 83, 90, 89, 100, 101, 108, 107, 118, 121, 126, 125, 136, 139, 146, 143, 156, 157, 164, 161, 174, 177, 182, 179, 192, 195, 202, 197, 212, 213, 220, 215, 230

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, Nov 19 2025: (Start)

a(n) = a(n-1) - a(n-3) + 2*a(n-4) - a(n-5) - a(n-6) + 2*a(n-7) - a(n-8) - a(n-9) + 2*a(n-10) - a(n-11) + a(n-13) - a(n-14) for n > 17.

G.f.: (-x^17 + x^16 - x^15 + 2*x^14 + 4*x^13 + 5*x^12 + 4*x^11 + 8*x^10 + 6*x^9 + 4*x^8 + 10*x^7 + 4*x^6 + 7*x^5 + 7*x^4 + 5*x^3 + 4*x^2 + 4*x + 1)/((x - 1)^2*(x + 1)^2*(x^2 + 1)^2*(x^2 - x + 1)*(x^4 - x^2 + 1)). (End)

Crossrefs

Sequence in context: A314694 A314695 A314696 * A187573 A314698 A314699

Adjacent sequences: A314694 A314695 A314696 * A314698 A314699 A314700

Keyword

nonn,more

Author

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

Status

approved