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%I #13 Feb 12 2018 12:34:55
%S 1,8,28,60,106,164,236,320,418,528,652,788,938,1100,1276,1464,1666,
%T 1880,2108,2348,2602,2868,3148,3440,3746,4064,4396,4740,5098,5468,
%U 5852,6248,6658,7080,7516,7964,8426,8900,9388,9888,10402,10928
%N Coordination sequence for "tsi" 3D uniform tiling.
%C First 20 terms computed by _Davide M. Proserpio_ using ToposPro.
%D B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #12.
%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/tsi">The tsi tiling (or net)</a>
%F Conjectures from _Colin Barker_, Feb 11 2018: (Start)
%F G.f.: (1 + 6*x + 12*x^2 + 6*x^3 + x^4) / ((1 - x)^3*(1 + x)).
%F a(n) = (13*n^2 + 4) / 2 for n>0 and even.
%F a(n) = (13*n^2 + 3) / 2 for n odd.
%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.
%F (End)
%Y See A299290 for partial sums.
%Y 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.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Feb 10 2018
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