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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved