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A047419
Numbers that are congruent to {1, 2, 3, 4, 6} mod 8.
1
1, 2, 3, 4, 6, 9, 10, 11, 12, 14, 17, 18, 19, 20, 22, 25, 26, 27, 28, 30, 33, 34, 35, 36, 38, 41, 42, 43, 44, 46, 49, 50, 51, 52, 54, 57, 58, 59, 60, 62, 65, 66, 67, 68, 70, 73, 74, 75, 76, 78, 81, 82, 83, 84, 86, 89, 90, 91, 92, 94, 97, 98, 99, 100, 102
OFFSET
1,2
FORMULA
G.f.: x*(1+x)*(2*x^4+x^2+1) / ( (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 - 40 - 2*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((n+3) mod 5) - 7*((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-7. (End)
a(n) = (2/25)*(20*n-20+5*cos(2*Pi*(n-1)/5)-2*cos(2*Pi*n/5)-2*cos(4*Pi*n/5)- 4*cos(2*Pi*(n+1)/5)-2*cos(Pi*(2*n+1)/5)+2*cos(2*Pi*(2*n+1)/5)-5*cos(Pi*(4*n+1)/5)+sin(Pi*(4*n+3)/10)+4*sin(Pi*(8*n+3)/10)-sin(Pi*(8*n+1)/10)). - Wesley Ivan Hurt, Oct 10 2018
MAPLE
A047419:=n->8*floor(n/5)+[(1, 2, 3, 4, 6)][(n mod 5)+1]: seq(A047419(n), n=0..100); # Wesley Ivan Hurt, Aug 08 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Aug 08 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 6, 9}, 100] (* Vincenzo Librandi, Aug 08 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 2, 3, 4, 6]]; // Wesley Ivan Hurt, Aug 08 2016
(GAP) Filtered([1..103], n->n mod 8 = 1 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
Sequence in context: A082976 A343382 A242407 * A135205 A145733 A356896
KEYWORD
nonn,easy
STATUS
approved