A047504 Numbers that are congruent to {1, 2, 3, 4, 5, 7} mod 8.

1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 39, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 63, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 84, 85, 87

Offset

1,2

Links

Table of n, a(n) for n=1..66.

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

Formula

G.f.: x*(1+x^2+x^4+x^5) / ( (x^2-x+1)*(1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015

From Wesley Ivan Hurt, Jun 16 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.

a(n) = (12*n-9+sqrt(3)*(3*sin(n*Pi/3)+sin(2*n*Pi/3)))/9.

a(6k) = 8k-1, a(6k-1) = 8k-3, a(6k-2) = 8k-4, a(6k-3) = 8k-5, a(6k-4) = 8k-6, a(6k-5) = 8k-7. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)+1)*Pi/16 + (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2-sqrt(2))/4. - Amiram Eldar, Dec 28 2021

Maple

A047504:=n->(12*n-9+sqrt(3)*(3*sin(n*Pi/3)+sin(2*n*Pi/3)))/9: seq(A047504(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [1, 2, 3, 4, 5, 7]]; // Wesley Ivan Hurt, Jun 16 2016

Crossrefs

Cf. A047451 (complement), A047422, A047519.

Sequence in context: A153350 A191919 A039055 * A359830 A088962 A047363

Adjacent sequences: A047501 A047502 A047503 * A047505 A047506 A047507

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved