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 A299289 Coordination sequence for "tsi" 3D uniform tiling. 51
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First 20 terms computed by Davide M. Proserpio using ToposPro. 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) 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) 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. Sequence in context: A045850 A264354 A033580 * A212515 A007331 A002408 Adjacent sequences:  A299286 A299287 A299288 * A299290 A299291 A299292 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 10 2018 STATUS approved

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Last modified January 17 23:59 EST 2021. Contains 340249 sequences. (Running on oeis4.)