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%I #36 May 07 2024 04:52:26
%S 1,7,22,47,82,127,182,247,322,407,502,607,722,847,982,1127,1282,1447,
%T 1622,1807,2002,2207,2422,2647,2882,3127,3382,3647,3922,4207,4502,
%U 4807,5122,5447,5782,6127,6482,6847,7222,7607,8002,8407,8822,9247,9682,10127,10582
%N a(0) = 1, a(n) = 5*n^2 + 2 for n>0.
%C Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3^3.4^2 2D tiling (cf. A008706). - _N. J. A. Sloane_, Feb 07 2018
%D B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #13.
%H Bruno Berselli, <a href="/A010001/b010001.txt">Table of n, a(n) for n = 0..1000</a>
%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/svk">The svk tiling (or net)</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (1+x)*(1+3*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012
%F E.g.f.: (x*(x+1)*5+2)*e^x-1. - _Gopinath A. R._, Feb 14 2012
%F Sum_{n>=0} 1/a(n) = 3/4+sqrt(10)/20*Pi*coth( Pi/5 *sqrt 10) = 1.2657655... - _R. J. Mathar_, May 07 2024
%t lst={};Do[AppendTo[lst,5*n^2+2],{n,0,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 15 2009 *)
%t Join[{1}, 5 Range[46]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)
%o (PARI) A010001(n)=5*n^2+2-!n \\ _M. F. Hasler_, Feb 14 2012
%Y Cf. A008706, A206399.
%Y See A063489 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_
%E More terms from _Bruno Berselli_, Feb 06 2012