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A047412 Numbers that are congruent to {0, 1, 2, 4, 6} mod 8. 2
0, 1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 17, 18, 20, 22, 24, 25, 26, 28, 30, 32, 33, 34, 36, 38, 40, 41, 42, 44, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 62, 64, 65, 66, 68, 70, 72, 73, 74, 76, 78, 80, 81, 82, 84, 86, 88, 89, 90, 92, 94, 96, 97, 98, 100, 102, 104, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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*(1+x+2*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 - 55 - 2*(n mod 5) - 2*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((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-6, a(5*k-3) = 8*k-7, a(5*k-4) = 8*k-8. (End)

a(n) = (40*n-55+6*cos(2*Pi*(n-1)/5)+2*cos(2*Pi*n/5)+2*cos(4*Pi*n/5)-2*cos(2*Pi*(n+1)/5)-6*cos(Pi*(4*n+1)/5)+6*sin(Pi*(4*n+3)/10)+2*sin(Pi*(8*n+3)/10)-6*sin(Pi*(8*n+1)/10))/25. - Wesley Ivan Hurt, Oct 10 2018

MAPLE

A047412:=n->8*floor(n/5)+[(0, 1, 2, 4, 6)][(n mod 5)+1]: seq(A047412(n), n=0..100); # Wesley Ivan Hurt, Aug 08 2016

MATHEMATICA

Flatten[Table[8*n + {0, 1, 2, 4, 6}, {n, 0, 11}]] (* Alonso del Arte, Sep 21 2011 *)

Select[Range[0, 150], MemberQ[{0, 1, 2, 4, 6}, Mod[#, 8]] &] (* Vincenzo Librandi, Mar 01 2016 *)

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 6, 8}, 100] (* Harvey P. Dale, Aug 06 2018 *)

PROG

(PARI) a(n)=n\5*8 + [0, 1, 2, 4, 6][n%5+1] \\ Charles R Greathouse IV, Oct 27 2015

(MAGMA) [n : n in [0..140] | n mod 8 in [0, 1, 2, 4, 6] ]; // Vincenzo Librandi, Mar 01 2016

(GAP) Filtered([0..105], n->n mod 8 = 0 or n mod 8 = 1 or n mod 8 = 2 or n mod 8 = 4 or n mod 8 = 6); # Muniru A Asiru, Oct 23 2018

CROSSREFS

Sequence in context: A003254 A247875 A153184 * A282760 A296214 A325572

Adjacent sequences:  A047409 A047410 A047411 * A047413 A047414 A047415

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 20 10:17 EDT 2019. Contains 326149 sequences. (Running on oeis4.)