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 A299254 #26 Jan 16 2025 06:55:46
%S A299254 1,7,21,45,79,122,175,237,309,391,482,583,693,813,943,1082,1231,1389,
%T A299254 1557,1735,1922,2119,2325,2541,2767,3002,3247,3501,3765,4039,4322,
%U A299254 4615,4917,5229,5551,5882,6223,6573,6933,7303,7682,8071,8469,8877,9295,9722,10159,10605,11061,11527,12002
%N A299254 Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3^4.6 2D tiling (cf. A250120).
%D A299254 B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #17.
%H A299254 Colin Barker, <a href="/A299254/b299254.txt">Table of n, a(n) for n = 0..1000</a>
%H A299254 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/svj">The svj tiling (or net)</a>
%H A299254 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F A299254 G.f.: (x^2+x+1)*(x^4+3*x^3+3*x+1)*(x+1) / ((x^4+x^3+x^2+x+1)*(1-x)^3). (This is the product of the g.f.'s for A250120 and A040000. - _N. J. A. Sloane_, Nov 10 2018)
%F A299254 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 07 2018
%F A299254 a(n) = 2*((sqrt(5) - 5)*(5 + 12*n^2) - (sqrt(5) - 1)*cos(2*n*Pi/5) + (sqrt(5) - 1)*cos(4*n*Pi/5))/(5*(sqrt(5) - 5)) for n > 0. - _Stefano Spezia_, Jun 06 2024
%t A299254 LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {1, 7, 21, 45, 79, 122, 175, 237}, 50] (* _Paolo Xausa_, Jan 16 2025 *)
%o A299254 (PARI) Vec((1 + x)*(1 + x + x^2)*(1 + 3*x + 3*x^3 + x^4) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ _Colin Barker_, Feb 07 2018
%Y A299254 Cf. A040000, A250120.
%Y A299254 Partial sums: A299260.
%Y A299254 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 A299254 nonn,easy
%O A299254 0,2
%A A299254 _N. J. A. Sloane_, Feb 06 2018