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%I #14 Feb 12 2018 12:34:55
%S 1,8,30,68,126,180,286,348,510,572,798,852,1150,1188,1566,1580,2046,
%T 2028,2590,2532,3198,3092,3870,3708,4606,4380,5406,5108,6270,5892,
%U 7198,6732,8190,7628,9246,8580,10366,9588,11550,10652,12798,11772,14110,12948,15486,14180
%N Coordination sequence for "reo" 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 #7.
%H Colin Barker, <a href="/A299279/b299279.txt">Table of n, a(n) for n = 0..1000</a>
%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/reo">The reo tiling (or net)</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F G.f.: (4*x^7 - 3*x^6 + 39*x^4 + 44*x^3 + 27*x^2 + 8*x + 1) / (1 - x^2)^3.
%F From _Colin Barker_, Feb 11 2018: (Start)
%F a(n) = 8*n^2 - 2 for n>1.
%F a(n) = 7*n^2 + 5 for n>1.
%F a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>7.
%F (End)
%o (PARI) Vec((1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^3*(1 + x)^3) + O(x^60)) \\ _Colin Barker_, Feb 11 2018
%Y See A299280 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,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 10 2018
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