A016897 a(n) = 5*n + 4.

4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 89, 94, 99, 104, 109, 114, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 244, 249, 254, 259, 264, 269, 274, 279, 284

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

[5*n+4: n in [0..70]]; // Vincenzo Librandi, May 02 2011

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 *)

PARI

a(n)=5*n+4 \\ Charles R Greathouse IV, Sep 24 2015

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