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A047393
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Numbers that are congruent to {0, 1} mod 8.
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8
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0, 1, 8, 9, 16, 17, 24, 25, 32, 33, 40, 41, 48, 49, 56, 57, 64, 65, 72, 73, 80, 81, 88, 89, 96, 97, 104, 105, 112, 113, 120, 121, 128, 129, 136, 137, 144, 145, 152, 153, 160, 161, 168, 169, 176, 177, 184, 185, 192, 193, 200, 201, 208, 209, 216, 217, 224, 225, 232
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OFFSET
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1,3
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COMMENTS
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Numbers k such that floor(k/2) = 4*floor(k/8). - Bruno Berselli, Oct 05 2017
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LINKS
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FORMULA
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a(n) = 4*n - 11/2 - 3*(-1)^n/2.
G.f.: x^2*(1+7*x) / ( (1+x)*(x-1)^2 ). (End)
Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)+1)*Pi/16 + log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 18 2021
E.g.f.: ((8*x - 3)*exp(x) + 3*exp(-x))/2 = 4*x*exp(x) - 3*sinh(x). - David Lovler, Aug 02 2022
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+8 od: seq(a[n], n=0..58); # Zerinvary Lajos, Mar 16 2008
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PROG
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(PARI) a(n) = 4*n - 11/2 - 3*(-1)^n/2; \\ David Lovler, Jul 25 2022
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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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EXTENSIONS
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STATUS
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approved
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