A047348 Numbers that are congruent to {2, 4} mod 7.

2, 4, 9, 11, 16, 18, 23, 25, 30, 32, 37, 39, 44, 46, 51, 53, 58, 60, 65, 67, 72, 74, 79, 81, 86, 88, 93, 95, 100, 102, 107, 109, 114, 116, 121, 123, 128, 130, 135, 137, 142, 144, 149, 151, 156, 158, 163, 165, 170

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Also, integer values of (n*(n+1)+1)/7. - Bruno Berselli, Jan 25 2013

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

seq(7*floor((n-1)/2)+3 +(-1)^n,n=1..49); # Gary Detlefs, Mar 02 2010

Mathematica

LinearRecurrence[{1,1,-1},{2,4,9},50] (* Harvey P. Dale, Aug 04 2016 *)

PARI

a(n) = (14*n - 9 - 3*(-1)^n)/4 \\ David Lovler, Sep 18 2022

Formula

From R. J. Mathar, Dec 16 2009: (Start)

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

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

a(n) = 7*floor((n-1)/2) + 3 + (-1)^n. - Gary Detlefs, Mar 02 2010

a(n) = 7*n - a(n-1) - 8 with n > 1, a(1)=2. - Vincenzo Librandi, Aug 05 2010

E.g.f.: 3 + ((14*x - 9)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 12 2022