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
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..10001
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]] (* or *) LinearRecurrence[{1, 1, -1}, {0, 3, 5}, 60] (* Harvey P. Dale, Apr 02 2017 *)
PROG
(PARI) forstep(n=0, 200, [3, 2], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved