A008857 a(n) = floor(n/9)*ceiling(n/9).

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 6, 6, 6, 6, 6, 9, 12, 12, 12, 12, 12, 12, 12, 12, 16, 20, 20, 20, 20, 20, 20, 20, 20, 25, 30, 30, 30, 30, 30, 30, 30, 30, 36, 42, 42, 42, 42, 42, 42, 42, 42, 49, 56, 56, 56, 56, 56, 56, 56, 56

Offset

0,11

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,-1,1).

Formula

From G. C. Greubel, Sep 13 2019: (Start)

a(n) = a(n-1) + 2*a(n-9) - 2*a(n-10) - a(n-18) + a(n-19).

G.f.: x^9*(1+x)/((1-x)*(1-x^9)^2). (End)

Maple

seq(coeff(series(x^9*(1+x)/((1-x)*(1-x^9)^2), x, n+1), x, n), n = 0..60); # G. C. Greubel, Sep 13 2019

Mathematica

CoefficientList[Series[x^9*(1+x)/((1-x)*(1-x^9)^2), {x, 0, 60}], x] (* G. C. Greubel, Sep 13 2019 *)

Prog

(PARI) my(x='x+O('x^60)); concat(vector(9), Vec(x^9*(1+x)/((1-x)*(1-x^9)^2))) \\ G. C. Greubel, Sep 13 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); [0, 0, 0, 0, 0, 0, 0, 0, 0] cat Coefficients(R!( x^9*(1+x)/((1-x)*(1-x^9)^2) )); // G. C. Greubel, Sep 13 2019
(Sage) [floor(n/9)*ceil(n/9) for n in (0..60)] # G. C. Greubel, Sep 13 2019
(GAP) a:=[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4];; for n in [20..60] do a[n]:=a[n-1]+2*a[n-9]-2*a[n-10]-a[n-18]+a[n-19]; od; a; # G. C. Greubel, Sep 13 2019

Crossrefs

Sequence in context: A064128 A248774 A104274 * A244463 A307590 A307987

Adjacent sequences: A008854 A008855 A008856 * A008858 A008859 A008860

Keyword

nonn

Author

N. J. A. Sloane

Status

approved