A313577 Coordination sequence Gal.4.97.3 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, 5, 10, 14, 19, 25, 29, 35, 39, 42, 51, 52, 59, 64, 65, 77, 76, 84, 88, 89, 102, 99, 109, 112, 113, 128, 123, 133, 137, 136, 153, 147, 157, 162, 160, 179, 170, 182, 186, 183, 205, 193, 207, 211, 207, 230, 217, 231, 235, 231

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, Apr 16 2024: (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) + 2*a(n-9) + a(n-10) + a(n-11) + a(n-12) + a(n-13) - a(n-14) - a(n-15) - a(n-16) - a(n-17) - a(n-18) for n > 18.

G.f.: (x + 1)^2*(x^16 + 4*x^15 + 7*x^14 + 12*x^13 + 18*x^12 + 24*x^11 + 25*x^10 + 32*x^9 + 28*x^8 + 32*x^7 + 25*x^6 + 24*x^5 + 18*x^4 + 12*x^3 + 7*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + x + 1)*(x^6 + x^3 + 1)*(x^4 + x^3 + x^2 + x + 1)^2). (End)

Crossrefs

Sequence in context: A313574 A313575 A313576 * A313578 A313579 A313580

Adjacent sequences: A313574 A313575 A313576 * A313578 A313579 A313580

Keyword

nonn,changed

Author

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

Status

approved