A047505 - OEIS

A047505

Numbers that are congruent to {0, 1, 2, 3, 6, 7} mod 8.

0, 1, 2, 3, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 46, 47, 48, 49, 50, 51, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 78, 79, 80, 81, 82, 83, 86, 87, 88

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..67.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

FORMULA

G.f.: x^2*(1+x+x^2+3*x^3+x^4+x^5) / ( (1+x)*(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) = a(n-1) + a(n-6) - a(n-7) for n>7.

a(n) = (24*n-27-3*cos(n*Pi)+12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18.

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

Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + (12-sqrt(2))*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - Amiram Eldar, Dec 26 2021

MAPLE

A047505:=n->(24*n-27-3*cos(n*Pi)+12*cos(n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047505(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)

PROG

(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 2, 3, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016

CROSSREFS

Cf. A047450, A047490.

Sequence in context: A039102 A287103 A050023 * A039071 A272799 A300157

Adjacent sequences: A047502 A047503 A047504 * A047506 A047507 A047508

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved