A047418 Numbers that are congruent to {0, 2, 3, 4, 6} mod 8.

0, 2, 3, 4, 6, 8, 10, 11, 12, 14, 16, 18, 19, 20, 22, 24, 26, 27, 28, 30, 32, 34, 35, 36, 38, 40, 42, 43, 44, 46, 48, 50, 51, 52, 54, 56, 58, 59, 60, 62, 64, 66, 67, 68, 70, 72, 74, 75, 76, 78, 80, 82, 83, 84, 86, 88, 90, 91, 92, 94, 96, 98, 99, 100, 102

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

G.f.: x^2*(2 + x + x^2 + 2*x^3 + 2*x^4)/((x^4 + x^3 + x^2 + x + 1)*(x - 1)^2). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, Aug 08 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.

a(n) = (40*n - 45 - 2*(n mod 5) + 3*((n + 1) mod 5) + 3*((n + 2) mod 5) - 2*((n + 3) mod 5) - 2*((n + 4) mod 5))/25.

a(5*k) = 8*k - 2, a(5*k-1) = 8*k - 4, a(5*k-2) = 8*k - 5, a(5*k-3) = 8*k - 6, a(5*k-4) = 8*k - 8. (End)

a(n) = (40*n - 45 + 2*cos(2*Pi*(n - 1)/5) - 2*cos(2*Pi*n/5) - 2*cos(4*Pi*n/5) - 6*cos(2*Pi*(n + 1)/5) - 6*cos(Pi*(2*n + 1)/5) + 6*cos(2*Pi*(2*n + 1)/5) - 2*cos(Pi*(4*n + 1)/5) + 6*sin(Pi*(8*n + 3)/10))/25. - Wesley Ivan Hurt, Oct 10 2018

Maple

A047418:=n->8*floor(n/5)+[(0, 2, 3, 4, 6)][(n mod 5)+1]: seq(A047418(n), n=0..100); # Wesley Ivan Hurt, Aug 08 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 2, 3, 4, 6}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 2, 3, 4, 6, 8}, 70] (* Harvey P. Dale, Oct 01 2015 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3, 4, 6]]; // Wesley Ivan Hurt, Aug 08 2016
(GAP) Filtered([0..103], n->n mod 8 = 0 or n mod 8 = 2 or n mod 8 = 3 or n mod 8 = 4 or n mod 8 = 6); # Muniru A Asiru, Oct 23 2018

Crossrefs

Cf. A047412, A047434, A047486, A047489, A047501, A047511, A047584.

Sequence in context: A121539 A257457 A122138 * A335999 A026508 A184103

Adjacent sequences: A047415 A047416 A047417 * A047419 A047420 A047421

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved