A110533 a(n) = floor(n/2) * floor(n/5).

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, 65, 65, 70, 70, 90, 90, 96, 96, 102, 119, 126, 126, 133, 133, 160, 160, 168, 168, 176, 198, 207, 207, 216, 216, 250, 250, 260, 260, 270, 297, 308, 308, 319, 319, 360, 360, 372

Offset: 0

Author

Reinhard Zumkeller, Jul 25 2005

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

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

Programs

Mathematica

Table[Floor[n/2]*Floor[n/5], {n, 0, 50}] (* G. C. Greubel, Aug 30 2017 *)

PARI

for(n=0,50, print1(floor(n/2)*floor(n/5), ", ")) \\ G. C. Greubel, Aug 30 2017

Formula

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

From R. J. Mathar, Feb 20 2011: (Start)

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

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)

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