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A047215
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Numbers that are congruent to {0, 2} mod 5.
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34
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0, 2, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, 40, 42, 45, 47, 50, 52, 55, 57, 60, 62, 65, 67, 70, 72, 75, 77, 80, 82, 85, 87, 90, 92, 95, 97, 100, 102, 105, 107, 110, 112, 115, 117, 120, 122, 125, 127, 130, 132, 135, 137, 140, 142, 145, 147, 150, 152, 155, 157
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OFFSET
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0,2
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COMMENTS
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Number of partitions of 5n into exactly 2 parts. - Colin Barker, Mar 23 2015
Numbers k such that k^2/5 + k*(k + 1)/5 = k*(2*k + 1)/5 is a nonnegative integer. - Bruno Berselli, Feb 14 2017
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LINKS
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FORMULA
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a(n) = floor(5*n/2).
G.f.: x*(2 + 3*x)/((1 + x)*(1 - x)^2).
a(n) = 5*n/2 + ((-1)^n-1)/4.
a(n+1) - a(n) = A010693(n+1). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = log(5)/4 - sqrt(5)*log(phi)/10 + sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021
E.g.f.: (5*x*exp(x) - sinh(x))/2. - David Lovler, Aug 22 2022
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MATHEMATICA
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Table[Floor[5 n/2], {n, 0, 100}] (* or *) LinearRecurrence[{1, 1, -1}, {0, 2, 5}, 101] (* Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)
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PROG
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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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