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 A016897 #92 Feb 16 2025 08:32:33
%S A016897 4,9,14,19,24,29,34,39,44,49,54,59,64,69,74,79,84,89,94,99,104,109,
%T A016897 114,119,124,129,134,139,144,149,154,159,164,169,174,179,184,189,194,
%U A016897 199,204,209,214,219,224,229,234,239,244,249,254,259,264,269,274,279,284
%N A016897 a(n) = 5*n + 4.
%C A016897 Except for 1, 2, n such that Sum_{k=1..n} (k mod 5)*C(n,k) is a power of 2. - _Benoit Cloitre_, Oct 17 2002
%C A016897 Numbers ending in 4 or 9. - _Lekraj Beedassy_, Jul 08 2006
%C A016897 The set of numbers congruent to 4 mod 5. - _Gary Detlefs_, Mar 07 2010
%C A016897 Also the number of (not necessarily maximal) cliques in the n-book graph and (n+1)-ladder graph. - _Eric W. Weisstein_, Nov 29 2017
%H A016897 Vincenzo Librandi, <a href="/A016897/b016897.txt">Table of n, a(n) for n = 0..2000</a>
%H A016897 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=944">Encyclopedia of Combinatorial Structures 944</a>.
%H A016897 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A016897 Leo Tavares, <a href="/A016897/a016897_1.jpg">Illustration: Mirror Triangles</a>.
%H A016897 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BookGraph.html">Book Graph</a>.
%H A016897 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Clique.html">Clique</a>.
%H A016897 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>.
%H A016897 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A016897 G.f.: (4+x)/(1-x)^2. - _Paul Barry_, Feb 27 2003
%F A016897 a(n) = 2*a(n-1) - a(n-2), n>1. - _Philippe Deléham_, Nov 03 2008
%F A016897 a(n) = A131098(n+2) + n + 1. - _Jaroslav Krizek_, Aug 15 2009
%F A016897 a(n) = 10*n - a(n-1) + 3, n>0. - _Vincenzo Librandi_, Nov 20 2010
%F A016897 A000041(a(n)) == 0 mod 5 is the first of Ramanujan's congruences. - _Ivan N. Ianakiev_, Dec 29 2014
%F A016897 a(n) = (n+2)^2 - 2*A000217(n-1). See Mirror Triangles illustration. - _Leo Tavares_, Aug 18 2021
%F A016897 Sum_{n>=0} (-1)^n/a(n) = sqrt(10*(5+sqrt(5)))*Pi/50 - log(2)/5 - sqrt(5)*log(phi)/5, where phi is the golden ratio (A001622). - _Amiram Eldar_, Dec 07 2021
%F A016897 E.g.f.: exp(x)*(4 + 5*x). - _Elmo R. Oliveira_, Mar 08 2024
%p A016897 a[1]:=4:for n from 2 to 100 do a[n]:=a[n-1]+5 od: seq(a[n], n=1..57); # _Zerinvary Lajos_, Mar 16 2008
%t A016897 Range[4, 500, 5] (* _Vladimir Joseph Stephan Orlovsky_, May 26 2011 *)
%t A016897 Table[5 n + 4, {n, 0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)
%t A016897 5 Range[0, 20] + 4 (* _Eric W. Weisstein_, Nov 29 2017 *)
%t A016897 LinearRecurrence[{2, -1}, {9, 14}, {0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)
%t A016897 CoefficientList[Series[(4 + x)/(-1 + x)^2, {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 29 2017 *)
%o A016897 (Magma) [5*n+4: n in [0..70]]; // _Vincenzo Librandi_, May 02 2011
%o A016897 (PARI) a(n)=5*n+4 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A016897 Cf. A001622, A008587, A016861, A016873, A016885.
%K A016897 nonn,easy
%O A016897 0,1
%A A016897 _N. J. A. Sloane_