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 A008253 #36 May 31 2022 11:37:57
%S A008253 1,4,12,24,42,64,92,124,162,204,252,304,362,424,492,564,642,724,812,
%T A008253 904,1002,1104,1212,1324,1442,1564,1692,1824,1962,2104,2252,2404,2562,
%U A008253 2724,2892,3064,3242,3424,3612,3804,4002,4204,4412,4624,4842,5064,5292,5524
%N A008253 Coordination sequence for diamond.
%D A008253 Inorganic Crystal Structure Database: Collection Code 9327.
%H A008253 N. J. A. Sloane, <a href="/A008253/b008253.txt">Table of n, a(n) for n = 0..1000</a>
%H A008253 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H A008253 R. 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), pp. 879-889.
%H A008253 Sean A. Irvine, <a href="/A008000/a008000_1.pdf">Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane</a>
%H A008253 M. O'Keeffe, M. A. Peskov, S. J. Ramsden, and O. M. Yaghi, <a href="https://dx.doi.org/10.1021/ar800124u">The reticular chemistry structure resource (RCSR) database of, and symbols for, crystal nets</a>, Accounts of Chemical Research, (2008), 1782-1789. See p. 1786.
%H A008253 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A008253 G.f.: (1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x)).
%F A008253 a(2*m) = 10*m^2+2, a(2*m+1) = 10*m^2+10*m+4 (_N. J. A. Sloane_).
%F A008253 Apart from first term, first differences of A007904(n). - _Alexander Adamchuk_, May 23 2006
%F A008253 a(n) = 2* ( 2 + Sum_{k=1..n-1} floor((5*k+3)/2) ). - _Alexander Adamchuk_, May 23 2006
%F A008253 From _Colin Barker_, Mar 21 2017: (Start)
%F A008253 a(n) = (5*n^2 + 4)/2 for n>0 and even.
%F A008253 a(n) = (5*n^2 + 3)/2 for n odd.
%F A008253 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.
%F A008253 (End)
%t A008253 {1}~Join~Table[2 (2 + Sum[Floor[(5 k + 3)/2], {k, n - 1}]), {n, 50}] (* _Alexander Adamchuk_, May 23 2006, edited by _Michael De Vlieger_, May 31 2022 *)
%o A008253 (PARI) Vec((1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ _Colin Barker_, Mar 21 2017
%Y A008253 Cf. A007904, A047209.
%K A008253 nonn,easy
%O A008253 0,2
%A A008253 _N. J. A. Sloane_, _Ralf W. Grosse-Kunstleve_