A047608 Numbers that are congruent to {4, 5} mod 8.

4, 5, 12, 13, 20, 21, 28, 29, 36, 37, 44, 45, 52, 53, 60, 61, 68, 69, 76, 77, 84, 85, 92, 93, 100, 101, 108, 109, 116, 117, 124, 125, 132, 133, 140, 141, 148, 149, 156, 157, 164, 165, 172, 173, 180, 181, 188, 189, 196, 197, 204, 205, 212, 213, 220, 221, 228, 229

Offset

1,1

Links

David Lovler, Table of n, a(n) for n = 1..10000

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

Formula

G.f.: x*(4+x+3*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Sep 22 2016

a(n) = 4n - 3*(1 + (-1)^n)/2 or a(n) = 4n - 3*((n-1) mod 2). - Heinz Ebert, Jul 12 2021

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)-1)*Pi/16 - log(2)/4 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 19 2021

E.g.f.: 3 + ((8*x - 3)*exp(x) - 3*exp(-x))/2. - David Lovler, Aug 20 2022

Mathematica

Select[Range[230], MemberQ[{4, 5}, Mod[#, 8]] &] (* Amiram Eldar, Dec 19 2021 *)

Prog

(PARI) a(n) = 4n - 3*(1 + (-1)^n)/2 \\ David Lovler, Aug 20 2022

Crossrefs

Union of A017113 and A004770.

Sequence in context: A330223 A325688 A080277 * A266725 A308783 A130011

Adjacent sequences: A047605 A047606 A047607 * A047609 A047610 A047611

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved