A314477 Coordination sequence Gal.5.193.4 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, 8, 14, 17, 22, 25, 34, 35, 44, 42, 51, 51, 62, 60, 74, 68, 79, 78, 90, 85, 103, 94, 108, 104, 119, 110, 132, 119, 137, 131, 147, 136, 161, 144, 165, 158, 176, 161, 191, 169, 193, 184, 205, 187, 220, 195, 221, 210, 233

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, May 14 2026: (Start)

a(n) = - 2*a(n-1) - 2*a(n-2) - a(n-3) + a(n-6) + 3*a(n-7) + 4*a(n-8) + 3*a(n-9) + a(n-10) - a(n-13) - 2*a(n-14) - 2*a(n-15) - a(n-16) for n > 18.

G.f.: (-x^18 - 3*x^17 - 2*x^16 + 7*x^15 + 24*x^14 + 47*x^13 + 72*x^12 + 100*x^11 + 127*x^10 + 146*x^9 + 148*x^8 + 137*x^7 + 116*x^6 + 92*x^5 + 66*x^4 + 41*x^3 + 20*x^2 + 7*x + 1)/((x - 1)^2*(x + 1)^2*(x^2 - x + 1)*(x^2 + x + 1)^2*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A020757 A361009 A314476 * A314478 A253195 A314479

Adjacent sequences: A314474 A314475 A314476 * A314478 A314479 A314480

Keyword

nonn

Author

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

Status

approved