OFFSET
1,2
COMMENTS
Also integers of the form sum(k = 1..n, k/7). - Alonso del Arte, Jan 20 2012
Sequence provides all integers m such that 56*m + 1 is a square. [Bruno Berselli, Oct 07 2015]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
G.f. -x^2*(3+x+3*x^2) / ( (1+x)^2*(x-1)^3 ). - R. J. Mathar, Jan 25 2011
a(n) = +1*a(n-1)+2*a(n-2)-2*a(n-3)-1*a(n-4)+1*a(n-5). - Joerg Arndt, Jan 25 2011
a(n) = (14*n*(n-1)+5*(2*n-1)*(-1)^n+5)/16. - Bruno Berselli, Jan 25 2011
a(n)-a(n-2) = A047341(n-1) for n>2. - Bruno Berselli, Jan 25 2011
Sum_{n>=2} 1/a(n) = 14 - 2*cot(Pi/7)*Pi. - Amiram Eldar, Mar 17 2022
MATHEMATICA
lst={}; s=0; Do[s+=n/7; If[Floor[s]==s, AppendTo[lst, s]], {n, 0, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 06 2009 *)
Select[Table[Plus@@Range[n]/7, {n, 0, 199}], IntegerQ] (* Alonso del Arte, Jan 20 2012 *)
CoefficientList[Series[-x (3 + x + 3 x^2) / ((1 + x)^2 (x - 1)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 3, 4, 13, 15}, 50] (* Harvey P. Dale, Sep 17 2023 *)
PROG
(PARI) a(n)=(14*n*(n-1)+5*(2*n-1)*(-1)^n+5)/16 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 04 2000
STATUS
approved