A047226 Numbers that are congruent to {0, 1, 2, 3, 4} mod 6; a(n)=floor(6(n-1)/5).

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A032766, A004773, A001068, this, A047368, A004777, A248375.

Programs

Magma

[n: n in [0..100] | n mod 6 in [0..4]]; // Vincenzo Librandi, Jan 06 2013

Maple

A047226 := proc(n)
    option remember;
    if n <= 6 then
        op(n,[0,1,2,3,4,6]) ;
    else
        procname(n-1)+procname(n-5)-procname(n-6) ;
    end if;
end proc: # R. J. Mathar, Jul 25 2013

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 4}, Mod[#, 6]]&] (* Vincenzo Librandi, Jan 06 2013 *)

Formula

G.f.: x^2*(1+x+x^2+x^3+2*x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Sep 17 2015, Jul 16 2013: (Start)

a(n) = floor( 6*(n-1)/5 ).

a(n) = a(n-1) + a(n-5) - a(n-6) for n>6.

a(n) = n - 1 + floor((n-1)/5). (End)

Sum_{n>=2} (-1)^n/a(n) = (9-4*sqrt(3))*Pi/36 + log(2+sqrt(3))/(2*sqrt(3)) + log(2)/6. - Amiram Eldar, Dec 17 2021

Extensions

Explicit formula added to definition by M. F. Hasler, Oct 05 2014