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A187322
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a(n) = floor(n/2) + floor(3*n/4).
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1
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0, 0, 2, 3, 5, 5, 7, 8, 10, 10, 12, 13, 15, 15, 17, 18, 20, 20, 22, 23, 25, 25, 27, 28, 30, 30, 32, 33, 35, 35, 37, 38, 40, 40, 42, 43, 45, 45, 47, 48, 50, 50, 52, 53, 55, 55, 57, 58, 60, 60, 62, 63, 65, 65, 67, 68, 70, 70, 72, 73, 75, 75, 77, 78, 80, 80, 82, 83, 85, 85, 87, 88, 90, 90, 92, 93, 95, 95, 97
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OFFSET
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0,3
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COMMENTS
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List of quadruples [5*k, 5*k, 5*k+2, 5*k+3]. - Luce ETIENNE, Aug 14 2017
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LINKS
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FORMULA
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a(n) = (10*n-5+3*cos(n*Pi)+2*(cos(n*Pi/2)-sin(n*Pi/2)))/8. - Luce ETIENNE, Aug 14 2017
G.f.: x^2*(2 + x + 2*x^2) / ((1 - x)^2*(1 + x)*(1 + x^2)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>4.
(End)
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MATHEMATICA
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Table[Floor[n/2]+Floor[3n/4], {n, 0, 120}]
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 0, 2, 3, 5}, 80] (* Harvey P. Dale, Dec 05 2018 *)
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PROG
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(PARI) concat(vector(2), Vec(x^2*(2 + x + 2*x^2) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^100))) \\ Colin Barker, Aug 14 2017
(Python)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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