OFFSET
1,2
COMMENTS
Also numbers k such that k*(k+2)*(k+4) is divisible by 7. - Bruno Berselli, Dec 28 2017
LINKS
Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
a(n) = 2*n + floor(n/3) + (n^2 mod 3), with offset 0, a(0)=0. - Gary Detlefs, Mar 19 2010
From Bruno Berselli, Mar 29 2011: (Start)
G.f.: x^2*(3 + 2*x + 2*x^2)/((1 - x)^2*(1 + x + x^2)).
a(n) = n + ceiling(4*(n-1)/3) - 1. - Arkadiusz Wesolowski, Sep 18 2012
a(n) = 2*(n-1) + ceiling((n-1)/3). - Karl V. Keller, Jr., Nov 01 2014
From Wesley Ivan Hurt, Jun 10 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 7*n/3 - 2 - 2*sin(2*n*Pi/3)/(3*sqrt(3)).
a(3*k) = 7*k-2, a(3*k-1) = 7*k-4, a(3*k-2) = 7*k-7. (End)
MAPLE
seq(2*n+floor(n/3)+(n^2 mod 3), n=0..52); # Gary Detlefs, Mar 19 2010
MATHEMATICA
Select[Range[0, 150], MemberQ[{0, 3, 5}, Mod[#, 7]]&] (* Harvey P. Dale, Dec 07 2011 *)
CoefficientList[Series[x (3 + 2 x + 2 x^2)/((1 - x)^2 (1 + x + x^2)), {x, 0, 70}], x] (* Vincenzo Librandi, Nov 02 2014 *)
PROG
(Magma) [n: n in [0..122] | n mod 7 in [0, 3, 5]]; // Bruno Berselli, Mar 29 2011
(Python)
import math
a = lambda n: 2*(n-1)+math.ceil((n-1)/3.0)
for n in range(1, 101): print(a(n), end = ", ") # Karl V. Keller, Jr., Nov 01 2014
(PARI) is(n)=!!setsearch([0, 3, 5], n%7) \\ Charles R Greathouse IV, Nov 09 2014
(PARI) a(n)=(7*n-5)\3 \\ Charles R Greathouse IV, Nov 09 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved