A047205 Numbers that are congruent to {0, 3, 4} mod 5.
0, 3, 4, 5, 8, 9, 10, 13, 14, 15, 18, 19, 20, 23, 24, 25, 28, 29, 30, 33, 34, 35, 38, 39, 40, 43, 44, 45, 48, 49, 50, 53, 54, 55, 58, 59, 60, 63, 64, 65, 68, 69, 70, 73, 74, 75, 78, 79, 80, 83, 84, 85, 88, 89, 90, 93, 94, 95, 98, 99, 100, 103, 104, 105, 108
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
Programs
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Magma
[ n : n in [0..150] | n mod 5 in [0, 3, 4] ]; // Vincenzo Librandi, Mar 31 2011
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Maple
A047205:=n->(15*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047205(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
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Mathematica
Select[Range[0, 200], MemberQ[{0, 3, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *) -
PARI
a(n)=n\3*5+[-1,0,3][n%3+1] \\ Charles R Greathouse IV, Dec 22 2011
Formula
G.f.: x^2*(3+x+x^2) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (15*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 5k-1, a(3k-1) = 5k-2, a(3k-2) = 5k-5. (End)
Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/5 - sqrt(1-2/sqrt(5))*Pi/5. - Amiram Eldar, Jan 01 2022