A316068 Coordination sequence Gal.5.296.4 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, 6, 9, 17, 20, 24, 32, 37, 41, 48, 52, 52, 65, 69, 68, 82, 80, 85, 99, 96, 102, 110, 113, 117, 126, 130, 128, 147, 145, 142, 164, 154, 163, 181, 168, 178, 190, 191, 195, 206, 206, 200, 229, 223, 216, 246, 228, 239, 263, 244

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 18 2025: (Start)

a(n) = - 2*a(n-2) + a(n-3) - 3*a(n-4) + 3*a(n-5) - 3*a(n-6) + 5*a(n-7) - 4*a(n-8) + 6*a(n-9) - 4*a(n-10) + 6*a(n-11) - 4*a(n-12) + 5*a(n-13) - 3*a(n-14) + 3*a(n-15) - 3*a(n-16) + a(n-17) - 2*a(n-18) - a(n-20) for n > 20.

G.f.: (x^20 + 6*x^19 + 11*x^18 + 28*x^17 + 35*x^16 + 64*x^15 + 67*x^14 + 102*x^13 + 91*x^12 + 126*x^11 + 100*x^10 + 126*x^9 + 91*x^8 + 102*x^7 + 67*x^6 + 64*x^5 + 35*x^4 + 28*x^3 + 11*x^2 + 6*x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)^2*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)^2). (End)

Crossrefs

Sequence in context: A007262 A129317 A316067 * A327796 A229354 A316069

Adjacent sequences: A316065 A316066 A316067 * A316069 A316070 A316071

Keyword

nonn

Author

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

Status

approved