A047608 - OEIS

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

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

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