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A350520
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The number of degree-n^2 polynomials over Z/2Z that can be written as f(f(x)) where f is a polynomial.
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0
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1, 1, 3, 8, 14, 32, 60, 128, 248, 512, 1008, 2048, 4064, 8192, 16320, 32768, 65408, 131072, 261888, 524288, 1048064, 2097152, 4193280, 8388608, 16775168, 33554432, 67104768, 134217728, 268427264
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OFFSET
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0,3
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LINKS
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FORMULA
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Conjecture:
a(2n) = A033991(2^(n-1)) = 4^n - 2^(n-1) for n >= 1;
a(2n+1) = 2^(2n+1) for n >= 1.
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EXAMPLE
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For n = 2, there are a(2) = 3 degree 4 polynomials of the form f(f(x)):
x^4 = f(f(x)) when f(x) = x^2 or f(x) = x^2 + 1,
x^4 + x = f(f(x)) when f(x) = x^2 + x, and
x^4 + x + 1 = f(f(x)) when f(x) = x^2 + x + 1.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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