login
A047564
Numbers that are congruent to {1, 3, 4, 5, 6, 7} mod 8.
4
1, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 51, 52, 53, 54, 55, 57, 59, 60, 61, 62, 63, 65, 67, 68, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 83, 84, 85, 86, 87
OFFSET
1,2
FORMULA
From Chai Wah Wu, May 30 2016: (Start)
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6) for n>6.
G.f.: x*(x^5 + x^3 + x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)). (End)
From Wesley Ivan Hurt, Jun 16 2016: (Start)
a(n) = (12*n-3-sqrt(3)*(cos((1-4*n)*Pi/6)+3*cos((1+2*n)*Pi/6)))/9.
a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-5, a(6k-5) = 8k-7. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)+1)*Pi/16 + sqrt(2)*log(sqrt(2)+2)/4 - (sqrt(2)+3)*log(2)/8. - Amiram Eldar, Dec 28 2021
MAPLE
A047564:=n->(12*n-3-sqrt(3)*(cos((1-4*n)*Pi/6)+3*cos((1+2*n)*Pi/6)))/9: seq(A047564(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{1, 3, 4, 5, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)
CoefficientList[Series[(x^5 + x^3 + x + 1) / ((x - 1)^2 (x^2 - x + 1) (x^2 + x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 18 2016 *)
PROG
(Magma) [n : n in [0..100] | n mod 8 in [1, 3, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016
CROSSREFS
Sequence in context: A307712 A048869 A039051 * A154536 A298110 A091815
KEYWORD
nonn,easy
STATUS
approved