A016897 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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