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A123920 Number of numbers congruent to 2 or 4 mod 6 between n and 2n inclusive. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Odd a(n) = (2k - 1) for n = {6k - 5, 6k - 3), where k = 1,2,3,... Even 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
KEYWORD
nonn
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

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)