A310244 Coordination sequence Gal.6.45.2 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, 3, 7, 12, 16, 22, 27, 31, 32, 35, 41, 46, 50, 56, 61, 65, 64, 67, 75, 80, 84, 90, 95, 99, 96, 99, 109, 114, 118, 124, 129, 133, 128, 131, 143, 148, 152, 158, 163, 167, 160, 163, 177, 182, 186, 192, 197, 201, 192, 195

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, Jun 12 2025: (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 + 2*x^14 + 5*x^13 + 7*x^12 + 11*x^11 + 11*x^10 + 16*x^9 + 13*x^8 + 17*x^7 + 14*x^6 + 13*x^5 + 9*x^4 + 7*x^3 + 5*x^2 + 2*x + 1)/((x - 1)^2*(x + 1)*(x^2 + 1)^2*(x^4 + 1)^2). (End)

Crossrefs

Sequence in context: A084582 A072098 A184930 * A310245 A192740 A310246

Adjacent sequences: A310241 A310242 A310243 * A310245 A310246 A310247

Keyword

nonn

Author

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

Status

approved