A047212 Numbers that are congruent to {0, 2, 4} mod 5.
0, 2, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 25, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 64, 65, 67, 69, 70, 72, 74, 75, 77, 79, 80, 82, 84, 85, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 104, 105, 107
Offset: 1
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
Programs
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Magma
[n : n in [0..140] | n mod 5 in [0, 2, 4]]; // Vincenzo Librandi, Mar 31 2011
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Magma
&cat[[n, n+2, n+4]: n in [0..90 by 5]]; // Bruno Berselli, Mar 31 2011
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Maple
A047212:=n->floor((5*n-3)/3); seq(A047212(n), n=1..100); # Wesley Ivan Hurt, Nov 25 2013
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Mathematica
Select[Range[0, 200], MemberQ[{0, 2, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *) -
PARI
a(n)=n\3*5+[-1,0,2][n%3+1] \\ Charles R Greathouse IV, Mar 29 2012
Formula
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
G.f.: x^2*(2 + 2*x + x^2)/((1 - x)^2*(1 + x + x^2)). - Bruno Berselli, Mar 31 2011
a(n) = floor((5*n-3)/3). - Gary Detlefs, May 14 2011
a(n) = n + ceiling(2*(n-1)/3) - 1. - Arkadiusz Wesolowski, Sep 18 2012
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = (15*n - 12 + 3*cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/9.
a(3*k) = 5*k-1, a(3*k-1) = 5*k-3, a(3*k-2) = 5*k-5. (End)
Sum_{n>=2} (-1)^n/a(n) = log(2)/5 + arccosh(7/2)/(2*sqrt(5)) - sqrt(1-2*sqrt(5)/5)*Pi/5. - Amiram Eldar, Dec 10 2021
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