A047572 Numbers that are congruent to {1, 2, 4, 5, 6, 7} mod 8.

1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 81, 82, 84, 85, 86, 87

Offset

1,2

Links

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

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

Formula

From Wesley Ivan Hurt, Jun 16 2016: (Start)

G.f.: x*(1+x+2*x^2+x^3+x^4+x^5+x^6) / ((x-1)^2*(1+x+x^2+x^3+x^4+x^5)).

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

a(n) = (24*n-9-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18.

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

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

Maple

A047572:=n->(24*n-9-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047572(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

Select[Range[0, 100], MemberQ[{1, 2, 4, 5, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)

Prog

(PARI) a(n)=n\6*8+[-1, 1, 2, 4, 5, 6][n%6+1] \\ Charles R Greathouse IV, Feb 24 2015
(Magma) [n : n in [0..100] | n mod 8 in [1, 2, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016

Crossrefs

Cf. A047422, A047504, A047519.

Sequence in context: A188033 A187485 A039052 * A003233 A218544 A286045

Adjacent sequences: A047569 A047570 A047571 * A047573 A047574 A047575

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved