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A110533
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a(n) = floor(n/2) * floor(n/5).
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6
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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
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OFFSET
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0,6
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LINKS
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FORMULA
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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
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MATHEMATICA
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Table[Floor[n/2]*Floor[n/5], {n, 0, 50}] (* G. C. Greubel, Aug 30 2017 *)
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PROG
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(PARI) for(n=0, 50, print1(floor(n/2)*floor(n/5), ", ")) \\ G. C. Greubel, Aug 30 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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