A047280 Numbers that are congruent to {3, 6} mod 7.

3, 6, 10, 13, 17, 20, 24, 27, 31, 34, 38, 41, 45, 48, 52, 55, 59, 62, 66, 69, 73, 76, 80, 83, 87, 90, 94, 97, 101, 104, 108, 111, 115, 118, 122, 125, 129, 132, 136, 139, 143, 146, 150, 153, 157, 160, 164, 167, 171, 174, 178, 181, 185, 188, 192, 195, 199, 202

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

Maple

A047280:=n->4*n-1-floor(n/2); seq(A047280(k),k=1..100); # Wesley Ivan Hurt, Oct 16 2013

Mathematica

Flatten[#+{3,6}&/@(7Range[0,30])]  (* Harvey P. Dale, Jan 11 2011 *)

PARI

a(n) = 4*n - 1 - floor(n/2) \\ David Lovler, Sep 14 2022

Formula

a(n) = 7*n - a(n-1) - 5 with n > 1, a(1)=3. - Vincenzo Librandi, Aug 05 2010

G.f.: x*(3 + 3*x + x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

a(n) = 3*n + ceiling(n/2) - 1. - Arkadiusz Wesolowski, Sep 20 2012

a(n) = 4n - 1 - floor(n/2). - Wesley Ivan Hurt, Oct 16 2013

E.g.f.: 1 + ((14*x - 3)*exp(x) - exp(-x))/4. - David Lovler, Sep 14 2022