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A047479
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Numbers that are congruent to {0, 1, 5, 7} mod 8.
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1
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0, 1, 5, 7, 8, 9, 13, 15, 16, 17, 21, 23, 24, 25, 29, 31, 32, 33, 37, 39, 40, 41, 45, 47, 48, 49, 53, 55, 56, 57, 61, 63, 64, 65, 69, 71, 72, 73, 77, 79, 80, 81, 85, 87, 88, 89, 93, 95, 96, 97, 101, 103, 104, 105, 109, 111, 112, 113, 117, 119, 120, 121, 125
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = (-7-(-1)^n+(2-i)*(-i)^n+(2+i)*i^n+8*n)/4 where i=sqrt(-1).
G.f.: x^2*(1+4*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)
E.g.f.: (2 - sin(x) + 2*cos(x) + (4*x - 3)*sinh(x) + 4*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, Jun 02 2016
Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + (8-3*sqrt(2))*log(2)/16 + 3*sqrt(2)*log(2+sqrt(2))/8. - Amiram Eldar, Dec 20 2021
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MAPLE
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MATHEMATICA
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Select[Range[0, 300], MemberQ[{0, 1, 5, 7}, Mod[#, 8]]&] (* Vincenzo Librandi, May 16 2012 *)
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PROG
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(Magma) I:=[0, 1, 5, 7, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 16 2012
(PARI) my(x='x+O('x^100)); concat(0, Vec(x^2*(1+4*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Dec 24 2015
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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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