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A047293 Numbers that are congruent to {0, 2, 4, 6} mod 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 13 21:30 EDT 2021. Contains 345010 sequences. (Running on oeis4.)