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 A002081 M1113 N0426 #65 Dec 14 2023 06:17:01
%S A002081 2,4,8,16,22,24,28,36,42,44,48,56,62,64,68,76,82,84,88,96,102,104,108,
%T A002081 116,122,124,128,136,142,144,148,156,162,164,168,176,182,184,188,196,
%U A002081 202,204,208,216,222,224,228,236,242,244,248,256,262,264,268,276,282
%N A002081 Numbers congruent to {2, 4, 8, 16} (mod 20).
%C A002081 First differences are periodic, cf. A000689.
%D A002081 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002081 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002081 Reinhard Zumkeller, <a href="/A002081/b002081.txt">Table of n, a(n) for n = 0..10000</a>
%H A002081 C. Babbage, <a href="http://dx.doi.org/10.1080/14786442608674053">On the Determination of the General Term of a New Class of Infinite Series</a>, Trans. Camb. Phil. Soc., 2 (1827), 217-225 (see p. 220).
%H A002081 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A002081 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A002081 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A002081 G.f.: 2*(1+2*x^2+2*x^3)/((1-x)^2*(1+x^2)). - _Simon Plouffe_
%F A002081 a(n+4) = a(n) + 20 for n > 3. - _Reinhard Zumkeller_, Sep 15 2011
%F A002081 a(n) = 5*n + (1/2)*(3 + (-1)^n)*(-1)^(n(n+1)/2). - _Bruno Berselli_, Sep 15 2011
%F A002081 E.g.f.: 2*cos(x) - sin(x) + 5*x*exp(x). - _Ilya Gutkovskiy_, Aug 17 2016
%p A002081 A002081:=2*(1+2*z**2+2*z**3)/(z**2+1)/(z-1)**2; # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t A002081 Flatten[Table[20n + {2, 4, 8, 16}, {n, 0, 14}]] (* _Alonso del Arte_, Nov 30 2011 *)
%t A002081 LinearRecurrence[{2, -2, 2, -1},{2, 4, 8, 16},57] (* _Ray Chandler_, Aug 25 2015 *)
%t A002081 Select[Range[300],MemberQ[{2,4,8,16},Mod[#,20]]&] (* _Harvey P. Dale_, Jul 20 2021 *)
%o A002081 (PARI) a(n) = 5*n + [2,-1,-2,1][(n%4)+1] \\ _Ralf Stephan_, Jun 08 2005
%o A002081 (PARI) is(n) = n > 0 && setsearch([2,4,8,16], n%20) > 0 \\ _Rick L. Shepherd_, Aug 17 2016
%o A002081 (Haskell)
%o A002081 a002081 n = a002081_list
%o A002081 a002081_list = filter ((`elem` [2,4,8,16]) . (`mod` 20)) [1..]
%o A002081 -- _Reinhard Zumkeller_, Sep 15 2011
%Y A002081 Cf. A002082, A008587.
%K A002081 nonn,easy,nice
%O A002081 0,1
%A A002081 _N. J. A. Sloane_
%E A002081 More terms from Larry Reeves (larryr(AT)acm.org), Jul 31 2000