OFFSET
0,1
COMMENTS
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
Numbers ending in 4 or 9. - Lekraj Beedassy, Jul 08 2006
The set of numbers congruent to 4 mod 5. - Gary Detlefs, Mar 07 2010
Also the number of (not necessarily maximal) cliques in the n-book graph and (n+1)-ladder graph. - Eric W. Weisstein, Nov 29 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 944.
Tanya Khovanova, Recursive Sequences.
Leo Tavares, Illustration: Mirror Triangles.
Eric Weisstein's World of Mathematics, Book Graph.
Eric Weisstein's World of Mathematics, Clique.
Eric Weisstein's World of Mathematics, Ladder Graph.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: (4+x)/(1-x)^2. - Paul Barry, Feb 27 2003
a(n) = 2*a(n-1) - a(n-2), n>1. - Philippe Deléham, Nov 03 2008
a(n) = A131098(n+2) + n + 1. - Jaroslav Krizek, Aug 15 2009
a(n) = 10*n - a(n-1) + 3, n>0. - Vincenzo Librandi, Nov 20 2010
A000041(a(n)) == 0 mod 5 is the first of Ramanujan's congruences. - Ivan N. Ianakiev, Dec 29 2014
a(n) = (n+2)^2 - 2*A000217(n-1). See Mirror Triangles illustration. - Leo Tavares, Aug 18 2021
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
E.g.f.: exp(x)*(4 + 5*x). - Elmo R. Oliveira, Mar 08 2024
MAPLE
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
MATHEMATICA
Range[4, 500, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
Table[5 n + 4, {n, 0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
5 Range[0, 20] + 4 (* Eric W. Weisstein, Nov 29 2017 *)
LinearRecurrence[{2, -1}, {9, 14}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[(4 + x)/(-1 + x)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)
PROG
(Magma) [5*n+4: n in [0..70]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=5*n+4 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved