A299289 Coordination sequence for "tsi" 3D uniform tiling.
1, 8, 28, 60, 106, 164, 236, 320, 418, 528, 652, 788, 938, 1100, 1276, 1464, 1666, 1880, 2108, 2348, 2602, 2868, 3148, 3440, 3746, 4064, 4396, 4740, 5098, 5468, 5852, 6248, 6658, 7080, 7516, 7964, 8426, 8900, 9388, 9888, 10402, 10928
Offset: 0
Keywords
References
- B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #12.
Links
- Reticular Chemistry Structure Resource (RCSR), The tsi tiling (or net)
Crossrefs
See A299290 for partial sums.
The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e: A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.
Formula
Conjectures from Colin Barker, Feb 11 2018: (Start)
G.f.: (1 + 6*x + 12*x^2 + 6*x^3 + x^4) / ((1 - x)^3*(1 + x)).
a(n) = (13*n^2 + 4) / 2 for n>0 and even.
a(n) = (13*n^2 + 3) / 2 for n odd.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4. (End)
Conjectured e.g.f.: ((4 + 13*x + 13*x^2)*cosh(x) + (3 + 13*x + 13*x^2)*sinh(x) - 2)/2. - Stefano Spezia, Jun 08 2024
Comments