A047428 Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 8.

0, 1, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 32, 33, 35, 36, 37, 38, 40, 41, 43, 44, 45, 46, 48, 49, 51, 52, 53, 54, 56, 57, 59, 60, 61, 62, 64, 65, 67, 68, 69, 70, 72, 73, 75, 76, 77, 78, 80, 81, 83, 84, 85, 86, 88

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+2*x+x^2+x^3+x^4+2*x^5) / ((1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2). - R. J. Mathar, Dec 07 2011

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

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

Sum_{n>=2} (-1)^n/a(n) = sqrt(2)*Pi/16 + log(2)/8 - sqrt(2)*log(99-70*sqrt(2))/16. - Amiram Eldar, Dec 27 2021

Maple

A047428:=n->(24*n-27-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047428(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 3, 4, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)

Prog

(Magma) [n : n in [0..100] | n mod 8 in [0, 1, 3, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 16 2016

Crossrefs

Cf. A047517, A047585.

Sequence in context: A306588 A353300 A219636 * A218784 A039066 A304800

Adjacent sequences: A047425 A047426 A047427 * A047429 A047430 A047431

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved