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A123919 Number of numbers congruent to 2 or 4 mod 6 and <= n. 3
0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

First differences of A056827. - R. J. Mathar, Nov 22 2008

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

From R. J. Mathar, Nov 22 2008: (Start)

G.f.: x^2*(1+x^2)/((1+x)*(1-x)^2*(1+x+x^2)*(1-x+x^2)).

a(n+1) - a(n) = A120325(n+1). (End)

MAPLE

seq(coeff(series(x^2*(1+x^2)/((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]; Array[f, 80] (* Robert G. Wilson v Oct 29 2006 *)

LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 1, 2, 2, 2, 2}, 80] (* G. C. Greubel, Aug 07 2019 *)

PROG

(PARI) my(x='x+O('x^80)); concat([0], Vec(x^2*(1+x^2)/((1-x)*(1-x^6)))) \\ G. C. Greubel, Aug 07 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 80); [0] cat Coefficients(R!( x^2*(1+x^2)/((1-x)*(1-x^6)) )); // G. C. Greubel, Aug 07 2019

(Sage)

def A123919_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( x^2*(1+x^2)/((1-x)*(1-x^6)) ).list()

a=A123919_list(80); a[1:] # G. C. Greubel, Aug 07 2019

(GAP) a:=[0, 1, 1, 2, 2, 2, 2];; 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. A047235.

Sequence in context: A189671 A109497 A156078 * A194324 A194328 A194304

Adjacent sequences:  A123916 A123917 A123918 * A123920 A123921 A123922

KEYWORD

easy,nonn

AUTHOR

Giovanni Teofilatto, Oct 29 2006

STATUS

approved

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)