A311714 Coordination sequence Gal.6.435.5 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, 13, 16, 21, 26, 29, 33, 37, 41, 44, 48, 53, 57, 62, 67, 71, 75, 79, 83, 86, 89, 94, 98, 102, 107, 111, 116, 120, 124, 128, 131, 136, 140, 144, 148, 152, 157, 160, 164, 168, 172, 177, 181, 186, 190, 194, 199, 202

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, Dec 29 2021: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 9*a(n-8) + 10*a(n-9) - 10*a(n-10) + 10*a(n-11) - 10*a(n-12) + 10*a(n-13) - 9*a(n-14) + 8*a(n-15) - 7*a(n-16) + 6*a(n-17) - 5*a(n-18) + 4*a(n-19) - 3*a(n-20) + 2*a(n-21) - a(n-22) for n > 22.

G.f.: (x^22 + 2*x^21 + 3*x^20 + 5*x^19 + 3*x^18 + 10*x^17 + 3*x^16 + 13*x^15 + 4*x^14 + 16*x^13 + 4*x^12 + 16*x^11 + 4*x^10 + 16*x^9 + 4*x^8 + 13*x^7 + 3*x^6 + 10*x^5 + 3*x^4 + 5*x^3 + 3*x^2 + 2*x + 1)/((x - 1)^2*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)*(x^6 - x^5 + 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: A311711 A311712 A311713 * A311715 A311716 A311717

Adjacent sequences: A311711 A311712 A311713 * A311715 A311716 A311717

Keyword

nonn

Author

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

Status

approved