A047356 Numbers that are congruent to {1, 3} mod 7.

1, 3, 8, 10, 15, 17, 22, 24, 29, 31, 36, 38, 43, 45, 50, 52, 57, 59, 64, 66, 71, 73, 78, 80, 85, 87, 92, 94, 99, 101, 106, 108, 113, 115, 120, 122, 127, 129, 134, 136, 141, 143, 148, 150, 155, 157, 162, 164, 169

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

This sequence is related to A010702 by a(n) = (Sum_{i=1..n} A010702(i)) - A010702(n+1). - Bruno Berselli, Mar 12 2012

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A010702.

Programs

Mathematica

With[{c=7 Range[0,50]},Sort[Join[c+1,c+3]]] (* or *) LinearRecurrence[ {1,1,-1},{1,3,8},100] (* Harvey P. Dale, May 29 2012 *)

PARI

a(n) = (14*n - 13 - 3*(-1)^n)/4 \\ David Lovler, Sep 11 2022

Formula

a(n) = 7*n - a(n-1) - 10 with n > 1, a(1)=1. - Vincenzo Librandi, Aug 05 2010

From R. J. Mathar, Oct 08 2011: (Start)

a(n) = 7*n/2 - 13/4 - 3*(-1)^n/4.

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

E.g.f.: 4 + ((14*x - 13)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 11 2022