A316022 Coordination sequence Gal.6.377.6 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, 6, 9, 15, 15, 21, 30, 27, 36, 39, 54, 51, 51, 63, 69, 66, 78, 72, 93, 93, 81, 105, 108, 99, 120, 105, 132, 135, 111, 147, 147, 132, 162, 138, 171, 177, 141, 189, 186, 165, 204, 171, 210, 219, 171, 231, 225, 198, 246, 204

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, Aug 01 2021: (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 > 22.

G.f.: (-6*x^22 + 6*x^21 - 6*x^20 + 6*x^18 - 12*x^17 + 12*x^16 - 5*x^15 + 17*x^14 - 8*x^13 + 29*x^12 - 8*x^11 + 29*x^10 + 7*x^9 + 20*x^8 + 14*x^7 + 13*x^6 + 17*x^5 + 4*x^4 + 11*x^3 + 4*x^2 + 5*x + 1)/((x - 1)^2*(x + 1)*(x^2 + 1)^2*(x^4 + 1)^2). (End)

Crossrefs

Sequence in context: A242042 A316021 A185398 * A316023 A139322 A139321

Adjacent sequences: A316019 A316020 A316021 * A316023 A316024 A316025

Keyword

nonn

Author

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

Status

approved