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 A016897 a(n) = 5*n + 4. 40
 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 CROSSREFS Cf. A001622, A008587, A016861, A016873, A016885. Sequence in context: A313116 A228176 A313117 * A189517 A190056 A313118 Adjacent sequences: A016894 A016895 A016896 * A016898 A016899 A016900 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified August 10 05:56 EDT 2024. Contains 375044 sequences. (Running on oeis4.)