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A047493
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Numbers that are congruent to {1, 4, 5, 7} mod 8.
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1
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1, 4, 5, 7, 9, 12, 13, 15, 17, 20, 21, 23, 25, 28, 29, 31, 33, 36, 37, 39, 41, 44, 45, 47, 49, 52, 53, 55, 57, 60, 61, 63, 65, 68, 69, 71, 73, 76, 77, 79, 81, 84, 85, 87, 89, 92, 93, 95, 97, 100, 101, 103, 105, 108, 109, 111, 113, 116, 117, 119, 121, 124
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(1+3*x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-3+i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).
E.g.f.: (2 - cos(x) + (4*x - 2)*sinh(x) + (4*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+3)*Pi/16 + log(2)/4 + sqrt(2)*log(sqrt(2)-1)/8. - Amiram Eldar, Dec 24 2021
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MAPLE
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 5, 7, 9}, 80] (* Harvey P. Dale, May 05 2018 *)
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PROG
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(Magma) [n : n in [0..150] | n mod 8 in [1, 4, 5, 7]]; // Wesley Ivan Hurt, May 26 2016
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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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