OFFSET
1,2
COMMENTS
Equivalently, numbers ending in 1, 2, 6 and 7. - Bruno Berselli, Sep 04 2018
LINKS
David Lovler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 5*n-a(n-1)-7 for n>1, with a(1)=1. - Vincenzo Librandi, Aug 05 2010
G.f.: x*(1+x+3*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Bruno Berselli, Mar 10 2012: (Start)
a(n) = (10*n-3*(-1)^n-9)/4.
From Wesley Ivan Hurt, Dec 29 2016: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3.
a(2*k) = 5*k-3, a(2*k-1) = 5*k-4. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2-2*sqrt(5)/5)*Pi/10 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021
E.g.f.: 3 + ((5*x - 9/2)*exp(x) - (3/2)*exp(-x))/2. - David Lovler, Aug 23 2022
MAPLE
MATHEMATICA
Select[Range[0, 200], MemberQ[{1, 2}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)
PROG
(PARI) a(n)=(n-1)\2*5+2-n%2 \\ Charles R Greathouse IV, Dec 22 2011
(Magma) [(10*n-3*(-1)^n-9)/4 : n in [1..100]]; // Wesley Ivan Hurt, Dec 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved