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A106450
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a(n) = A004443(n) if n is odd, a(n) = A004443(n)/2 if n is even.
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2
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2, 3, 0, 1, 3, 7, 2, 5, 5, 11, 4, 9, 7, 15, 6, 13, 9, 19, 8, 17, 11, 23, 10, 21, 13, 27, 12, 25, 15, 31, 14, 29, 17, 35, 16, 33, 19, 39, 18, 37, 21, 43, 20, 41, 23, 47, 22, 45, 25, 51, 24, 49, 27, 55, 26, 53, 29, 59, 28, 57, 31, 63, 30, 61, 33, 67, 32, 65, 35, 71, 34, 69, 37, 75
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OFFSET
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0,1
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LINKS
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FORMULA
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a(4*n+1) = 4*n+3, a(4*n+2) = 2*n, a(4*n+3) = 4*n+1, a(4*n+4) = 2*n+3.
a(n) = ((2+4*i)*(-i)^n+(2-4*i)*i^n-(-3+(-1)^n)*n)/4 for n>0 where i is the imaginary unit.
a(n) = a(n-2)+a(n-4)-a(n-6) for n>6.
G.f.: (2+3*x-2*x^2-2*x^3+x^4+3*x^5+x^6) / ((1-x)^2*(1+x)^2*(1+x^2)).
(End)
a(n) = (4*floor(1/(n+1)) - (-1)^n*n + 3*n + 8*sin((Pi*n)/2) + 4*cos((Pi*n)/2))/4.
E.g.f.: 1 + cos(x) + x*cosh(x) + 2*sin(x) + x*sinh(x)/2. (End)
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PROG
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(PARI) Vec((2+3*x-2*x^2-2*x^3+x^4+3*x^5+x^6)/((1-x)^2*(1+x)^2*(1+x^2)) + O(x^50)) \\ Colin Barker, Apr 19 2016
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CROSSREFS
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Skipping the initial term (a(0)=2), this is row 2 of A106449.
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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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