A047293 Numbers that are congruent to {0, 2, 4, 6} mod 7.

0, 2, 4, 6, 7, 9, 11, 13, 14, 16, 18, 20, 21, 23, 25, 27, 28, 30, 32, 34, 35, 37, 39, 41, 42, 44, 46, 48, 49, 51, 53, 55, 56, 58, 60, 62, 63, 65, 67, 69, 70, 72, 74, 76, 77, 79, 81, 83, 84, 86, 88, 90, 91, 93, 95, 97, 98, 100, 102, 104, 105, 107, 109, 111

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A047276, A047345.

Programs

Magma

I:=[0, 2, 4, 6, 7]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, Apr 26 2012

Maple

A047293:=n->2*n-2-floor((n-1)/4): seq(A047293(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

Mathematica

Select[Range[0,100],MemberQ[{0,2,4,6},Mod[#,7]]&] (* Vincenzo Librandi, Apr 26 2012 *)
LinearRecurrence[{1,0,0,1,-1},{0,2,4,6,7},80] (* Harvey P. Dale, Jun 21 2019 *)

PARI

A047293(n)=n*7\4-1  \\ M. F. Hasler, Apr 27 2012

Formula

a(n) = floor(ceiling((7n + 2)/2)/2).

a(n) = 2n-2-floor((n-1)/4). - Gary Detlefs, Mar 27 2010

From Colin Barker, Mar 13 2012: (Start)

a(n) = a(n-1)+a(n-4)-a(n-5) for n>5.

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

From Wesley Ivan Hurt, May 21 2016: (Start)

a(n) = (14n-11+i^(2n)+(1-i)*i^(-n)+(1+i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047276(n), a(2n-1) = A047345(n). (End)