A047288 Numbers that are congruent to {4, 6} mod 7.

4, 6, 11, 13, 18, 20, 25, 27, 32, 34, 39, 41, 46, 48, 53, 55, 60, 62, 67, 69, 74, 76, 81, 83, 88, 90, 95, 97, 102, 104, 109, 111, 116, 118, 123, 125, 130, 132, 137, 139, 144, 146, 151, 153, 158, 160, 165, 167, 172

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

LinearRecurrence[{1,1,-1},{4,6,11},50] (* Harvey P. Dale, Jan 18 2013 *)

PARI

a(n) = (-1 - 3*(-1)^n + 14*n)/4 \\ David Lovler, Sep 15 2022

Formula

a(n) = 7*n - a(n-1) - 4 with n > 1, a(1)=4. - Vincenzo Librandi, Aug 05 2010

From Colin Barker, Mar 13 2012: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3).

G.f.: x*(4 + 2*x + x^2)/((1-x)^2*(1+x)). (End)

a(n) = (-1 - 3*(-1)^n + 14*n)/4. - Colin Barker, May 14 2012

a(n) = floor(7*n/2) - (-1)^n. - Wesley Ivan Hurt, Sep 12 2017

E.g.f.: 1 + ((14*x - 1)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 15 2022