%I #91 Mar 08 2024 18:22:25

%S 4,9,14,19,24,29,34,39,44,49,54,59,64,69,74,79,84,89,94,99,104,109,

%T 114,119,124,129,134,139,144,149,154,159,164,169,174,179,184,189,194,

%U 199,204,209,214,219,224,229,234,239,244,249,254,259,264,269,274,279,284

%N a(n) = 5*n + 4.

%C 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 Numbers ending in 4 or 9. - _Lekraj Beedassy_, Jul 08 2006

%C The set of numbers congruent to 4 mod 5. - _Gary Detlefs_, Mar 07 2010

%C 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 Vincenzo Librandi, <a href="/A016897/b016897.txt">Table of n, a(n) for n = 0..2000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=944">Encyclopedia of Combinatorial Structures 944</a>.

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

%H Leo Tavares, <a href="/A016897/a016897_1.jpg">Illustration: Mirror Triangles</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BookGraph.html">Book Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: (4+x)/(1-x)^2. - _Paul Barry_, Feb 27 2003

%F a(n) = 2*a(n-1) - a(n-2), n>1. - _Philippe Deléham_, Nov 03 2008

%F a(n) = A131098(n+2) + n + 1. - _Jaroslav Krizek_, Aug 15 2009

%F a(n) = 10*n - a(n-1) + 3, n>0. - _Vincenzo Librandi_, Nov 20 2010

%F A000041(a(n)) == 0 mod 5 is the first of Ramanujan's congruences. - _Ivan N. Ianakiev_, Dec 29 2014

%F a(n) = (n+2)^2 - 2*A000217(n-1). See Mirror Triangles illustration. - _Leo Tavares_, Aug 18 2021

%F 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 E.g.f.: exp(x)*(4 + 5*x). - _Elmo R. Oliveira_, Mar 08 2024

%p 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 Range[4, 500, 5] (* _Vladimir Joseph Stephan Orlovsky_, May 26 2011 *)

%t Table[5 n + 4, {n, 0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)

%t 5 Range[0, 20] + 4 (* _Eric W. Weisstein_, Nov 29 2017 *)

%t LinearRecurrence[{2, -1}, {9, 14}, {0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)

%t CoefficientList[Series[(4 + x)/(-1 + x)^2, {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 29 2017 *)

%o (Magma) [5*n+4: n in [0..70]]; // _Vincenzo Librandi_, May 02 2011

%o (PARI) a(n)=5*n+4 \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Cf. A001622, A008587, A016861, A016873, A016885.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_