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

1,1

Links

David Lovler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A285415 A275668 A212537 * A263652 A285679 A093661

Adjacent sequences: A047386 A047387 A047388 * A047390 A047391 A047392

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved