A311627 Coordination sequence Gal.6.190.1 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, 4, 8, 12, 18, 24, 29, 32, 35, 41, 47, 52, 54, 56, 62, 69, 76, 79, 81, 86, 91, 97, 100, 103, 109, 114, 120, 123, 127, 134, 138, 142, 143, 147, 156, 162, 167, 167, 170, 179, 185, 190, 189, 191, 200, 207, 214, 214, 216, 224

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, Mar 06 2022: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 3*a(n-3) - 3*a(n-4) + 4*a(n-5) - 5*a(n-6) + 6*a(n-7) - 6*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 3*a(n-13) - 3*a(n-14) + 2*a(n-15) - a(n-16) for n > 16.

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

Crossrefs

Sequence in context: A311624 A311625 A311626 * A311628 A311629 A311630

Adjacent sequences: A311624 A311625 A311626 * A311628 A311629 A311630

Keyword

nonn

Author

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

Status

approved