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A008497
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a(n) = floor(n/5)*floor((n+1)/5).
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2
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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, 30, 36, 36, 36, 36, 42, 49, 49, 49, 49, 56, 64, 64, 64, 64, 72, 81, 81, 81, 81, 90, 100, 100, 100, 100, 110, 121, 121, 121, 121
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OFFSET
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0,10
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,2,-2,0,0,0,-1,1).
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FORMULA
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a(n)= a(n-1) + 2*a(n-5) - 2*a(n-6) - a(n-10) + a(n-11).
G.f.: x^5*(1+x^4)/ ((x^4+x^3+x^2+x+1)^2 * (1-x)^3). (End)
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MAPLE
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seq( mul(floor((n+j)/5), j=0..1), n=0..55); # G. C. Greubel, Nov 08 2019
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MATHEMATICA
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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 *)
Product[Floor[(Range[55] +j-1)/5], {j, 0, 1}] (* G. C. Greubel, Nov 08 2019 *)
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PROG
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(PARI) vector(56, n, prod(j=0, 1, (n+j-1)\5) ) \\ G. C. Greubel, Nov 08 2019
(Magma) [&*[Floor((n+j)/5): j in [0..1]]: n in [0..55]]; // G. C. Greubel, Nov 08 2019
(Sage) [product(floor((n+j)/5) for j in (0..1)) for n in (0..55)] # G. C. Greubel, Nov 08 2019
(GAP) List([0..55], n-> Int(n/5)*Int((n+1)/5) ); # G. C. Greubel, Nov 08 2019
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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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