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

1,2

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A047276, A047345.

Sequence in context: A198081 A081223 A184654 * A191176 A184585 A287113

Adjacent sequences: A047290 A047291 A047292 * A047294 A047295 A047296

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved