OFFSET
1,2
LINKS
G. C. Greubel, 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
From Chai Wah Wu, May 29 2016: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
G.f.: x^2*(4*x^5 + x^4 + 2*x^3 + x^2 + x + 3)/(x^7 - x^6 - x + 1). (End)
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = (12*n - 15 - cos(n*Pi) - 5*cos(n*Pi/3) - sqrt(3)*(2*cos((1-4*n)*Pi/6) - 3*sin(n*Pi/3)))/6.
a(6k) = 12k-4, a(6k-1) = 12k-5, a(6k-2) = 12k-7, a(6k-3) = 12k-8, a(6k-4) = 12k-9, a(6k-5) = 12k-12. (End)
Sum_{n>=2} (-1)^n/a(n) = (15-8*sqrt(3))*Pi/72 + log(2)/4. - Amiram Eldar, Dec 31 2021
MAPLE
A154571:=n->(12*n-15-cos(n*Pi)-5*cos(n*Pi/3)-sqrt(3)*(2*cos((1-4*n)*Pi/6)-3*sin(n*Pi/3)))/6: seq(A154571(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 3, 4, 5, 7, 8, 12}, 50] (* G. C. Greubel, May 29 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 12 in [0, 3, 4, 5, 7, 8]]; // Wesley Ivan Hurt, May 29 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jan 12 2009
STATUS
approved