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*(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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved