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

1,2

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).

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

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 *)

Prog

(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
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( x*(1+x-x^2+x^3)/((1-x)*(1-x^6)) )); // G. C. Greubel, Aug 07 2019
(Sage)
def A123920_list(prec):
    P.<x> = 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
(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

Crossrefs

Cf. A123919.

Sequence in context: A030361 A060715 A108954 * A322141 A029170 A079526

Adjacent sequences: A123917 A123918 A123919 * A123921 A123922 A123923

Keyword

nonn,easy

Author

Giovanni Teofilatto, Oct 29 2006

Extensions

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

More terms from Alexander Adamchuk, Nov 08 2006

Status

approved