A313426 Coordination sequence Gal.5.220.4 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, 10, 13, 19, 26, 29, 35, 40, 43, 48, 51, 60, 67, 67, 72, 77, 85, 90, 89, 96, 103, 110, 115, 115, 120, 125, 133, 140, 141, 144, 149, 160, 165, 163, 166, 173, 187, 190, 187, 192, 197, 210, 213, 211, 218, 221, 235, 240, 235

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, Dec 25 2021: (Start)

a(n) = - a(n-2) - a(n-4) + 2*a(n-5) - a(n-6) + 2*a(n-7) + 2*a(n-9) - a(n-10) + 2*a(n-11) - a(n-12) - a(n-14) - a(n-16) for n > 16.

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

Crossrefs

Sequence in context: A313424 A313425 A376341 * A313427 A313428 A313429

Adjacent sequences: A313423 A313424 A313425 * A313427 A313428 A313429

Keyword

nonn

Author

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

Status

approved