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a(n) = floor(n/9)*ceiling(n/9).
1

%I #12 Sep 08 2022 08:44:36

%S 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,

%T 12,12,12,12,16,20,20,20,20,20,20,20,20,25,30,30,30,30,30,30,30,30,36,

%U 42,42,42,42,42,42,42,42,49,56,56,56,56,56,56,56,56

%N a(n) = floor(n/9)*ceiling(n/9).

%H G. C. Greubel, <a href="/A008857/b008857.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,-1,1).

%F From _G. C. Greubel_, Sep 13 2019: (Start)

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

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

%p 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

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

%o (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

%o (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

%o (Sage) [floor(n/9)*ceil(n/9) for n in (0..60)] # _G. C. Greubel_, Sep 13 2019

%o (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

%K nonn

%O 0,11

%A _N. J. A. Sloane_