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 A299287 #25 Aug 29 2024 00:59:10
%S A299287 1,10,33,72,126,196,281,382,498,630,777,940,1118,1312,1521,1746,1986,
%T A299287 2242,2513,2800,3102,3420,3753,4102,4466,4846,5241,5652,6078,6520,
%U A299287 6977,7450,7938,8442,8961,9496,10046,10612,11193,11790,12402,13030,13673,14332
%N A299287 Coordination sequence for "tcd" 3D uniform tiling.
%C A299287 First 20 terms computed by _Davide M. Proserpio_ using ToposPro.
%H A299287 Colin Barker, <a href="/A299287/b299287.txt">Table of n, a(n) for n = 0..1000</a>
%H A299287 B. Grünbaum, <a href="https://faculty.washington.edu/moishe/branko/BG199.Uniform%20Tilings%20of%203-Space.pdf">Uniform tilings of 3-space</a>, Geombinatorics, 4 (1994), 49-56. See tiling #3.
%H A299287 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/tcd">The tcd tiling (or net)</a>
%H A299287 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A299287 G.f.: (x^4 + 8*x^3 + 13*x^2 + 8*x + 1) / ((1 + x)*(1 - x)^3).
%F A299287 From _Colin Barker_, Feb 11 2018: (Start)
%F A299287 a(n) = (31*n^2 + 8) / 4 for even n>0.
%F A299287 a(n) = (31*n^2 + 9) / 4 for odd n>0.
%F A299287 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4. (End)
%F A299287 E.g.f.: ((8 + 31*x + 31*x^2)*cosh(x) + (9 + 31*x + 31*x^2)*sinh(x) - 4)/4. - _Stefano Spezia_, Jun 08 2024
%t A299287 LinearRecurrence[{2, 0, -2, 1}, {1, 10, 33, 72, 126}, 50] (* _Paolo Xausa_, Aug 28 2024 *)
%o A299287 (PARI) Vec((1 + 8*x + 13*x^2 + 8*x^3 + x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ _Colin Barker_, Feb 11 2018
%Y A299287 See A299288 for partial sums.
%Y A299287 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 A299287 nonn,easy
%O A299287 0,2
%A A299287 _N. J. A. Sloane_, Feb 10 2018