A311542 Coordination sequence Gal.5.155.1 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, 17, 23, 26, 29, 36, 39, 43, 50, 52, 57, 61, 63, 73, 77, 75, 83, 91, 91, 95, 102, 105, 111, 114, 115, 127, 130, 125, 137, 146, 142, 147, 156, 159, 164, 165, 166, 182, 185, 175, 190, 201, 193, 200, 209, 211, 218

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 11 2025: (Start)

a(n) = - 3*a(n-2) + a(n-3) - 5*a(n-4) + 4*a(n-5) - 6*a(n-6) + 8*a(n-7) - 6*a(n-8) + 11*a(n-9) - 6*a(n-10) + 11*a(n-11) - 6*a(n-12) + 8*a(n-13) - 6*a(n-14) + 4*a(n-15) - 5*a(n-16) + a(n-17) - 3*a(n-18) - a(n-20) for n > 22.

G.f.: (-x^22 - x^21 - x^20 + 3*x^19 + 11*x^18 + 25*x^17 + 48*x^16 + 73*x^15 + 105*x^14 + 132*x^13 + 158*x^12 + 171*x^11 + 176*x^10 + 168*x^9 + 150*x^8 + 125*x^7 + 95*x^6 + 67*x^5 + 42*x^4 + 23*x^3 + 11*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)*(x^2 - x + 1)*(x^2 + x + 1)^2*(x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A311540 A311541 A036573 * A311543 A311544 A376651

Adjacent sequences: A311539 A311540 A311541 * A311543 A311544 A311545

Keyword

nonn,more

Author

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

Status

approved