A123920 Number of numbers congruent to 2 or 4 mod 6 between n and 2n inclusive.

1, 2, 1, 2, 2, 2, 3, 4, 3, 4, 4, 4, 5, 6, 5, 6, 6, 6, 7, 8, 7, 8, 8, 8, 9, 10, 9, 10, 10, 10, 11, 12, 11, 12, 12, 12, 13, 14, 13, 14, 14, 14, 15, 16, 15, 16, 16, 16, 17, 18, 17, 18, 18, 18, 19, 20, 19, 20, 20, 20, 21, 22, 21, 22, 22, 22, 23, 24, 23, 24, 24, 24, 25, 26, 25, 26, 26, 26

Offset: 1

Author

Giovanni Teofilatto, Oct 29 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Crossrefs

Cf. A123919.

Programs

GAP

a:=[1,2,1,2,2,2,3];; for n in [8..80] do a[n]:=a[n-1]+a[n-6]-a[n-7]; od; a; # G. C. Greubel, Aug 07 2019

Magma

R:=PowerSeriesRing(Integers(), 80); Coefficients(R!( x*(1+x-x^2+x^3)/((1-x)*(1-x^6)) )); // G. C. Greubel, Aug 07 2019

Maple

seq(coeff(series(x*(1+x-x^2+x^3)/((1-x)*(1-x^6)), x, n+1), x, n), n = 1..80); # G. C. Greubel, Aug 07 2019

Mathematica

f[n_]:= Floor[n/2] - Floor[n/6]; Table[f[2n] - f[n-1], {n, 80}] (* Robert G. Wilson v *)
Table[Count[Range[n,2n],?(MemberQ[{2,4},Mod[#,6]]&)],{n,80}] (* _Harvey P. Dale, Mar 25 2019 *)
LinearRecurrence[{1,0,0,0,0,1,-1}, {1,2,1,2,2,2,3}, 80] (* G. C. Greubel, Aug 07 2019 *)

PARI

my(x='x+O('x^80)); Vec(x*(1+x-x^2+x^3)/((1-x)*(1-x^6))) \\ G. C. Greubel, Aug 07 2019

Sage

def A123920_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(1+x-x^2+x^3)/((1-x)*(1-x^6)) ).list()
a=A123920_list(80); a[1:] # G. C. Greubel, Aug 07 2019

Formula

a(n) = 2k - 1 for n = {6k - 5, 6k - 3}, where k = 1,2,3,... a(n) = 2k for n = {6k - 4, 6k - 2, 6k - 1, 6k}, where k = 1,2,3,... - Alexander Adamchuk, Nov 08 2006

G.f.: x*(1+x-x^2+x^3)/((1-x)*(1-x^6)). - G. C. Greubel, Aug 07 2019

Extensions

Corrected and extended by Robert G. Wilson v, Oct 29 2006

More terms from Alexander Adamchuk, Nov 08 2006