A313150 Coordination sequence Gal.6.382.2 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, 4, 9, 14, 20, 26, 30, 35, 41, 45, 51, 57, 59, 64, 72, 75, 80, 89, 91, 93, 102, 107, 109, 117, 123, 124, 130, 138, 142, 146, 152, 157, 160, 165, 173, 178, 180, 187, 194, 195, 201, 210, 211, 214, 224, 228, 230, 239, 244, 245

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, Sep 12 2025: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 5*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 4*a(n-10) + 5*a(n-11) - 5*a(n-12) + 4*a(n-13) - 3*a(n-14) + 2*a(n-15) - a(n-16) for n > 19.

G.f.: (-x^19 + x^18 - x^17 + 2*x^16 + x^15 + 5*x^14 + 4*x^13 + 9*x^12 + 6*x^11 + 12*x^10 + 10*x^9 + 11*x^8 + 10*x^7 + 11*x^6 + 7*x^5 + 8*x^4 + 4*x^3 + 4*x^2 + 2*x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A184515 A313148 A313149 * A313151 A313152 A313153

Adjacent sequences: A313147 A313148 A313149 * A313151 A313152 A313153

Keyword

nonn

Author

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

Status

approved