A047374 Numbers that are congruent to {4, 5} mod 7.

4, 5, 11, 12, 18, 19, 25, 26, 32, 33, 39, 40, 46, 47, 53, 54, 60, 61, 67, 68, 74, 75, 81, 82, 88, 89, 95, 96, 102, 103, 109, 110, 116, 117, 123, 124, 130, 131, 137, 138, 144, 145, 151, 152, 158, 159, 165, 166, 172

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A017029, A017041.

Programs

Mathematica

Select[Range[200], MemberQ[{4, 5}, Mod[#, 7]] &] (* Amiram Eldar, May 07 2021 *)

PARI

a(n) = (14*n - 5*(-1)^n - 3)/4 \\ David Lovler, Sep 15 2022

Formula

G.f.: x*(4 + x + 2*x^2)/((1 + x)*(x - 1)^2). - R. J. Mathar, Dec 04 2011

a(n) = -(5/4)*(-1)^n + 7*(n-1)/2 + 11/4. - Viet Quoc Le Tran, Jun 14 2014

a(n) = (14*n - 5*(-1)^n - 3)/4. - David Lovler, Sep 15 2022

E.g.f.: 2 + ((14*x - 3)*exp(x) - 5*exp(-x))/4. - David Lovler, Sep 15 2022