0,2

First 20 terms computed by Davide M. Proserpio using ToposPro.

B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #12.

Reticular Chemistry Structure Resource (RCSR), The tsi tiling (or net)

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

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.

Sequence in context: A045850 A264354 A033580 * A212515 A342251 A007331

Adjacent sequences: A299286 A299287 A299288 * A299290 A299291 A299292

N. J. A. Sloane, Feb 10 2018

approved