A314807 Coordination sequence Gal.6.528.5 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, 5, 9, 14, 17, 22, 25, 30, 36, 40, 43, 49, 52, 57, 60, 65, 72, 75, 77, 84, 87, 92, 95, 100, 108, 110, 111, 119, 122, 127, 130, 135, 144, 145, 145, 154, 157, 162, 165, 170, 180, 180, 179, 189, 192, 197, 200, 205, 216, 215

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 13 2023: (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 + 4*x^14 + 6*x^13 + 7*x^12 + 11*x^11 + 10*x^10 + 15*x^9 + 15*x^8 + 19*x^7 + 11*x^6 + 14*x^5 + 8*x^4 + 9*x^3 + 5*x^2 + 4*x + 1)/((x - 1)^2*(x + 1)*(x^2 + 1)^2*(x^4 + 1)^2). (End)

Crossrefs

Sequence in context: A314804 A314805 A314806 * A314808 A314809 A314810

Adjacent sequences: A314804 A314805 A314806 * A314808 A314809 A314810

Keyword

nonn

Author

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

Status

approved