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a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5).
2

%I #16 Sep 08 2022 08:44:35

%S 0,0,0,0,0,1,1,1,2,4,8,8,8,12,18,27,27,27,36,48,64,64,64,80,100,125,

%T 125,125,150,180,216,216,216,252,294,343,343,343,392,448,512,512,512,

%U 576,648,729,729,729,810,900,1000

%N a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5).

%H G. C. Greubel, <a href="/A008496/b008496.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,3,-3,0,0,0,-3,3,0,0,0,1,-1).

%F From _R. J. Mathar_, Apr 16 2010: (Start)

%F a(n) = A002266(n)*A008497(n+1).

%F a(n) = a(n-1) +3*a(n-5) -3*a(n-6) -3*a(n-10) +3*a(n-11) +a(n-15) -a(n-16).

%F G.f.: x^5*(1+x+x^2)*(x^6-x^5+2*x^3-x+1)/((x^4+x^3+x^2+x+1)^3 *(x-1)^4). (End)

%p seq( mul(floor((n+j)/5), j=0..2), n=0..55); # _G. C. Greubel_, Nov 08 2019

%t LinearRecurrence[{1,0,0,0,3,-3,0,0,0,-3,3,0,0,0,1,-1}, {0,0,0,0,0,1,1,1, 2,4,8,8,8,12,18,27},60] (* or *) Table[Times@@Thread[Floor[(n +{0,1,2} )/5]],{n,0,60}] (* _Harvey P. Dale_, Apr 09 2018 *)

%t Product[Floor[(Range[55] +j-1)/5], {j,0,2}] (* _G. C. Greubel_, Nov 08 2019 *)

%o (PARI) vector(56, n, prod(j=0,2, (n+j-1)\5) ) \\ _G. C. Greubel_, Nov 08 2019

%o (Magma) [&*[Floor((n+j)/5): j in [0..2]]: n in [0..55]]; // _G. C. Greubel_, Nov 08 2019

%o (Sage) [product(floor((n+j)/5) for j in (0..2)) for n in (0..55)] # _G. C. Greubel_, Nov 08 2019

%o (GAP) List([0..55], n-> Int(n/5)*Int((n+1)/5)*Int((n+2)/5) ); # _G. C. Greubel_, Nov 08 2019

%Y Cf. A008382, A008497. - _R. J. Mathar_, Apr 16 2010

%K nonn

%O 0,9

%A _N. J. A. Sloane_