A110533 - OEIS

%I #15 Mar 30 2023 02:37:38

%S 0,0,0,0,0,2,3,3,4,4,10,10,12,12,14,21,24,24,27,27,40,40,44,44,48,60,

%T 65,65,70,70,90,90,96,96,102,119,126,126,133,133,160,160,168,168,176,

%U 198,207,207,216,216,250,250,260,260,270,297,308,308,319,319,360,360,372

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

%H G. C. Greubel, <a href="/A110533/b110533.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = A004526(n)*A002266(n).

%F From _R. J. Mathar_, Feb 20 2011: (Start)

%F a(n) = +a(n-2) +a(n-5) -a(n-7) +a(n-10) -a(n-12) -a(n-15) +a(n-17).

%F G.f.: -x^5*(2+3*x+x^2+x^3+x^4+4*x^5+3*x^6+x^7+x^8+x^9+x^10+x^11) / ( (x^4-x^3+x^2-x+1) *(1+x)^2 *(x^4+x^3+x^2+x+1)^2 *(x-1)^3 ). (End)

%F Sum_{n>=5} (-1)^(n+1)/a(n) = sqrt(5*(5-2*sqrt(5)))*Pi/8 - (5/8)*(1 + sqrt(5)*log(phi)) + (25/16)*log(5) - 2*log(2), where phi is the golden ratio (A001622). - _Amiram Eldar_, Mar 30 2023

%t Table[Floor[n/2]*Floor[n/5], {n, 0, 50}] (* _G. C. Greubel_, Aug 30 2017 *)

%o (PARI) for(n=0,50, print1(floor(n/2)*floor(n/5), ", ")) \\ _G. C. Greubel_, Aug 30 2017

%Y Cf. A001622, A002266, A004526, A010762, A110532.

%K nonn

%O 0,6

%A _Reinhard Zumkeller_, Jul 25 2005