A299910 Coordination sequence of point of type 3.3.4.3.4 in 3-uniform tiling #3.54 in the Galebach listing.
1, 5, 10, 17, 23, 28, 33, 40, 45, 48, 55, 63, 68, 71, 78, 85, 88, 93, 101, 108, 111, 116, 123, 128, 133, 139, 146, 151, 156, 161, 166, 173, 179, 184, 189, 196, 201, 204, 211, 219, 224, 227, 234, 241, 244, 249, 257, 264, 267, 272, 279, 284, 289, 295, 302, 307
Offset: 0
Keywords
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..2500
- Brian Galebach, Tiling 3.54
- Brian Galebach, Tiling 3.54 [Annotated figure showing the 3 kinds of points mentioned in A299909, A299910, A299911]
- Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers
- Printable Paper Web Site, Printable 3.3.3.3.3.3,3.3.4.3.4 Tessellation Small [Shows this tiling]
- Rémy Sigrist, PARI program for A299910
Programs
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PARI
\\ See Links section.
Formula
Conjectures from Chai Wah Wu, Jul 10 2025: (Start)
a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-7) - a(n-8) + a(n-9) - a(n-10) for n > 10.
G.f.: (x^10 + 4*x^9 + 6*x^8 + 11*x^7 + 11*x^6 + 12*x^5 + 11*x^4 + 11*x^3 + 6*x^2 + 4*x + 1)/(x^10 - x^9 + x^8 - x^7 - x^3 + x^2 - x + 1). (End)
Extensions
More terms from Rémy Sigrist, May 10 2021