OFFSET
1,3
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).
FORMULA
G.f.: x^2*(1+3*x+x^2+x^3+x^4+x^5) / ((1-x)^2*(1+x)*(1-x+x^2)*(1+x+x^2)). - Colin Barker, Jan 09 2016
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
a(n) = (24*n-15-3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/18.
a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-7, a(6k-5) = 8k-8. (End)
Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*Pi/16 + (14-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - Amiram Eldar, Dec 27 2021
MAPLE
A047569:=n->(24*n-15-3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/18: seq(A047569(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{0, 1, 4, 5, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 4, 5, 6, 7, 8}, 80] (* Harvey P. Dale, Feb 15 2024 *)
PROG
(PARI) concat(0, Vec(x^2*(1+3*x+x^2+x^3+x^4+x^5)/((1-x)^2*(1+x)*(1-x+x^2)*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Jan 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved