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 A008264 #69 Jan 08 2025 09:32:46
%S A008264 1,4,12,25,44,67,96,130,170,214,264,319,380,445,516,592,674,760,852,
%T A008264 949,1052,1159,1272,1390,1514,1642,1776,1915,2060,2209,2364,2524,2690,
%U A008264 2860,3036,3217,3404,3595,3792,3994,4202,4414,4632,4855,5084,5317,5556,5800
%N A008264 Coordination sequence for tridymite, lonsdaleite, and wurtzite.
%D A008264 Inorganic Crystal Structure Database: Collection Code 29343
%D A008264 Michael O'Keeffe, Topological and geometrical characterization of sites in silicon carbide polytypes, Chemistry of Materials 3 (2) (1991), 332-335. (Eq. (2) gives an empirical formula for a(n). - _N. J. A. Sloane_, Apr 07 2018)
%H A008264 Vincenzo Librandi, <a href="/A008264/b008264.txt">Table of n, a(n) for n = 0..1000</a>
%H A008264 M. L. Glasser, <a href="https://doi.org/10.1016/0022-3697(59)90080-0">Symmetry properties of the wurtzite structure</a>, Journal of Physics and Chemistry of Solids, 10(2-3) (1959), 229-241.
%H A008264 Ralf W. Grosse-Kunstleve, <a href="/A005897/a005897.html">Zeolites, Frameworks, Coordination Sequences and Encyclopedia of Integer Sequences</a>, 1996.
%H A008264 Ralf W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, <a href="http://neilsloane.com/doc/ac96cs/">Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites</a>, Acta Cryst., A52 (1996), 879-889.
%H A008264 Sean A. Irvine, <a href="/A008000/a008000_1.pdf">Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane</a>.
%H A008264 Michael O'Keeffe, <a href="https://doi.org/10.1107/S0108767391006633">N-dimensional diamond, sodalite and rare sphere packings</a>, Acta Cryst. A 47 (1991), 749-753.
%H A008264 Michael O'Keeffe, <a href="https://doi.org/10.1021/cm00014a025">Topological and geometrical characterization of sites in silicon carbide polytypes</a>, Chemistry of Materials 3 (2) (1991), 332-335.
%H A008264 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/lon">The lon net</a> (lonsdaleite) and <a href="http://rcsr.net/nets/lon-b">The lon-b net</a> (wurtzite).
%H A008264 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).
%F A008264 a(4*m+k) = 42*m^2 + 21*k*m + [ 2, 4, 12, 25 ], 0 <= k < 4 (_N. J. A. Sloane_).
%F A008264 a(n) = 1 + (42*n^2 + (1 + (-1)^n)*(3 + 2*(-1)^((n - 1)*n/2)) + 6)/16 for n > 0, a(0) = 1. - _Bruno Berselli_, Jul 24 2013
%F A008264 G.f.: (1 + 2*x + 5*x^2 + 5*x^3 + 5*x^4 + 2*x^5 + x^6)/((1 - x)^3*(1 + x + x^2 + x^3)). - _Bruno Berselli_, Jul 24 2013
%t A008264 a[n_] := (m = Quotient[n, 4]; k = Mod[n, 4]; 42*m^2 + 21*k*m + Switch[k, 0, 2, 1, 4, 2, 12, 3, 25]); a[0]=1; Table[a[n], {n, 0, 47}] (* _Jean-François Alcover_, Oct 11 2012, from the first formula *)
%t A008264 Join[{1}, Table[1 + (42 n^2 + (1 + (-1)^n) (3 + 2 (-1)^((n - 1) n/2)) + 6)/16, {n, 50}]] (* _Bruno Berselli_, Jul 24 2013 *)
%t A008264 LinearRecurrence[{2,-1,0,1,-2,1},{1,4,12,25,44,67,96},20] (* _Harvey P. Dale_, Dec 27 2016 *)
%o A008264 (PARI) a(n)=if(n, 1+(42*n^2+(1+(-1)^n)*(3+2*(-1)^((n-1)*n/2))+6)/16, 1) \\ _Charles R Greathouse IV_, Feb 10 2017
%Y A008264 Cf. A008524 for 4-D analog, A008253 for diamond.
%Y A008264 Cf. A217511 for theta series.
%K A008264 nonn,easy,nice
%O A008264 0,2
%A A008264 _Ralf W. Grosse-Kunstleve_