A311533 Coordination sequence Gal.4.51.1 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, 22, 27, 32, 36, 38, 41, 46, 52, 58, 63, 68, 69, 71, 75, 81, 89, 94, 99, 100, 102, 105, 110, 119, 125, 130, 130, 133, 136, 140, 149, 155, 161, 160, 163, 167, 171, 180, 185, 191, 190, 193, 197, 202, 212, 216

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, Jan 24 2020: (Start)

a(n) = - a(n-2) - a(n-4) - a(n-6) + 2*a(n-7) + 2*a(n-9) + 2*a(n-11) + 2*a(n-13) - a(n-14) - a(n-16) - a(n-18) - a(n-20) for n > 20.

G.f.: (x^20 + 4*x^19 + 9*x^18 + 17*x^17 + 26*x^16 + 38*x^15 + 53*x^14 + 68*x^13 + 80*x^12 + 86*x^11 + 89*x^10 + 86*x^9 + 80*x^8 + 68*x^7 + 53*x^6 + 38*x^5 + 26*x^4 + 16*x^3 + 9*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + 1)*(x^4 + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)^2). (End)

Crossrefs

Sequence in context: A311530 A311531 A311532 * A311534 A311535 A311536

Adjacent sequences: A311530 A311531 A311532 * A311534 A311535 A311536

Keyword

nonn

Author

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

Status

approved