A047389 Numbers that are congruent to {3, 5} mod 7.

3, 5, 10, 12, 17, 19, 24, 26, 31, 33, 38, 40, 45, 47, 52, 54, 59, 61, 66, 68, 73, 75, 80, 82, 87, 89, 94, 96, 101, 103, 108, 110, 115, 117, 122, 124, 129, 131, 136, 138, 143, 145, 150, 152, 157, 159, 164, 166, 171

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Mathematica

#+{3,5}&/@(7*Range[0,30])//Flatten (* Harvey P. Dale, Oct 10 2019 *)

PARI

a(n) = (14*n - 5 - 3*(-1)^n)/4 \\ David Lovler, Sep 13 2022

Formula

a(n) = 7*n - a(n-1) - 6, n > 1. - Vincenzo Librandi, Aug 05 2010

From Bruno Berselli, Sep 08 2010: (Start)

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

a(n) - a(n-1) - a(n-2) + a(n-3) = 0 for n > 3.

a(n) = (14*n - 5 - 3*(-1)^n)/4. (End)

E.g.f.: 2 + ((14*x - 5)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 13 2022