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A008497 a(n) = floor(n/5)*floor((n+1)/5).

%I A008497 #25 May 10 2025 03:12:28
%S A008497 0,0,0,0,0,1,1,1,1,2,4,4,4,4,6,9,9,9,9,12,16,16,16,16,20,25,25,25,25,
%T A008497 30,36,36,36,36,42,49,49,49,49,56,64,64,64,64,72,81,81,81,81,90,100,
%U A008497 100,100,100,110,121,121,121,121
%N A008497 a(n) = floor(n/5)*floor((n+1)/5).
%H A008497 G. C. Greubel, <a href="/A008497/b008497.txt">Table of n, a(n) for n = 0..1000</a>
%H A008497 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,2,-2,0,0,0,-1,1).
%F A008497 From _R. J. Mathar_, Apr 16 2010: (Start)
%F A008497 a(n) = A002266(n)*A002266(n+1).
%F A008497 a(n)= a(n-1) + 2*a(n-5) - 2*a(n-6) - a(n-10) + a(n-11).
%F A008497 G.f.: x^5*(1+x^4)/ ((x^4+x^3+x^2+x+1)^2 * (1-x)^3). (End)
%F A008497 From _Amiram Eldar_, May 10 2025: (Start)
%F A008497 Sum_{n>=5} 1/a(n) = 2*Pi^2/3 + 1.
%F A008497 Sum_{n>=5} (-1)^(n+1)/a(n) = 2*log(2)-1. (End)
%p A008497 seq( mul(floor((n+j)/5), j=0..1), n=0..55); # _G. C. Greubel_, Nov 08 2019
%t A008497 Times@@@Partition[Floor[Range[0,60]/5],2,1] (* or *) LinearRecurrence[ {1,0,0,0,2,-2,0,0,0,-1,1},{0,0,0,0,0,1,1,1,1,2,4},60] (* _Harvey P. Dale_, Feb 01 2015 *)
%t A008497 Product[Floor[(Range[55] +j-1)/5], {j,0,1}] (* _G. C. Greubel_, Nov 08 2019 *)
%o A008497 (PARI) a(n) = (n\5)*((n+1)\5); \\ _Michel Marcus_, Jan 06 2017
%o A008497 (PARI) vector(56, n, prod(j=0,1, (n+j-1)\5) ) \\ _G. C. Greubel_, Nov 08 2019
%o A008497 (Magma) [&*[Floor((n+j)/5): j in [0..1]]: n in [0..55]]; // _G. C. Greubel_, Nov 08 2019
%o A008497 (Sage) [product(floor((n+j)/5) for j in (0..1)) for n in (0..55)] # _G. C. Greubel_, Nov 08 2019
%o A008497 (GAP) List([0..55], n-> Int(n/5)*Int((n+1)/5) ); # _G. C. Greubel_, Nov 08 2019
%Y A008497 Cf. A002266.
%K A008497 nonn,easy
%O A008497 0,10
%A A008497 _N. J. A. Sloane_