OFFSET
1,2
COMMENTS
Multiples of 5 interleaved with 2 less than multiples of 5. - Wesley Ivan Hurt, Oct 19 2013
Numbers k such that k^2/5 + k*(k + 1)/10 = k*(3*k + 1)/10 is a nonnegative integer. - Bruno Berselli, Feb 14 2017
For n >= 2, also the vertex cover number of the (n-1)-necklace graph. - Eric W. Weisstein, Feb 17 2026
For n >= 4, also the diameter of the n-cube connected cycle graph. - Eric W. Weisstein, Feb 25 2026
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..10001
Eric Weisstein's World of Mathematics, Cube-Connected Cycle Graph.
Eric Weisstein's World of Mathematics, Graph Diameter.
Eric Weisstein's World of Mathematics, Necklace Graph.
Eric Weisstein's World of Mathematics, Vertex Cover Number.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 2*n - 5 + ceiling(n/2). - Jesus De Loera (deloera(AT)math.ucdavis.edu)
a(n) = 5*n - a(n-1) - 7 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010
From Bruno Berselli, Jun 28 2011: (Start)
G.f.: (2*x + 3)*x^2/((x + 1)*(x - 1)^2).
a(n) = (10*n + (-1)^n - 9)/4.
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=3 and b(k)=A020714(k-1)=5*2^(k-1) for k>0. - Philippe Deléham, Oct 17 2011
a(n) = n + ceiling(3*(n-1)/2) - 1. - Arkadiusz Wesolowski, Sep 18 2012
a(n) = floor(5*n/2)-2 = 3*n - 3 - floor((n-1)/2). - Wesley Ivan Hurt, Oct 14 2013
a(n+1) = n + (n + (n + (n mod 2))/2). - Wesley Ivan Hurt, Oct 19 2013
Sum_{n>=2} (-1)^n/a(n) = log(5)/4 - sqrt(5)*log(phi)/10 - sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021
E.g.f.: 2 + ((5*x - 9/2)*exp(x) + (1/2)*exp(-x))/2. - David Lovler, Aug 22 2022
MAPLE
seq(floor(5*k/2)-2, k=1..100); # Wesley Ivan Hurt, Sep 27 2013
MATHEMATICA
Select[Range[0, 200], MemberQ[{0, 3}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)
Table[Floor[5 n/2] - 2, {n, 100}] (* Wesley Ivan Hurt, Sep 27 2013 *)
With[{c5 = 5 Range[0, 30]}, Riffle[c5, c5 + 3]] (* Harvey P. Dale, Apr 02 2017 *)
LinearRecurrence[{1, 1, -1}, {0, 3, 5}, 60] (* Harvey P. Dale, Apr 02 2017 *)
Table[(10 n - 9 + (-1)^n)/4, {n, 20}] (* Eric W. Weisstein, Feb 17 2026 *)
CoefficientList[Series[x (3 + 2 x)/((-1 + x)^2 (1 + x)), {x, 0, 20}], x] (* Eric W. Weisstein, Feb 17 2026 *)
Floor[5 Range[20]/2] - 2 (* Eric W. Weisstein, Feb 25 2026 *)
PROG
(PARI) forstep(n=0, 200, [3, 2], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
