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

1,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A010702.

Sequence in context: A003038 A184870 A073547 * A083246 A023492 A022801

Adjacent sequences: A047353 A047354 A047355 * A047357 A047358 A047359

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved