This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A299258 #21 Jun 06 2024 14:20:20
%S A299258 1,5,13,25,41,62,89,121,157,197,242,293,349,409,473,542,617,697,781,
%T A299258 869,962,1061,1165,1273,1385,1502,1625,1753,1885,2021,2162,2309,2461,
%U A299258 2617,2777,2942,3113,3289,3469,3653,3842,4037,4237,4441,4649,4862,5081,5305,5533,5765,6002,6245,6493,6745
%N A299258 Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 4.6.12 2D tiling (cf. A072154).
%D A299258 B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #23.
%H A299258 Colin Barker, <a href="/A299258/b299258.txt">Table of n, a(n) for n = 0..1000</a>
%H A299258 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/fst">The fst tiling (or net)</a>
%H A299258 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F A299258 G.f.: (x^2+x+1)*(x^2-x+1)*(x+1)^3 / ((x^4+x^3+x^2+x+1)*(1-x)^3).
%F A299258 a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) for n>7. - _Colin Barker_, Feb 09 2018
%F A299258 a(n) ~ 12*n^2/5. - _Stefano Spezia_, Jun 06 2024
%t A299258 LinearRecurrence[{2,-1,0,0,1,-2,1},{1,5,13,25,41,62,89,121},60] (* _Harvey P. Dale_, Mar 14 2023 *)
%o A299258 (PARI) Vec((1 + x)^3*(1 - x + x^2)*(1 + x + x^2) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ _Colin Barker_, Feb 09 2018
%Y A299258 Cf. A072154.
%Y A299258 Partial sums: A299264.
%Y A299258 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 A299258 nonn,easy
%O A299258 0,2
%A A299258 _N. J. A. Sloane_, Feb 07 2018