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A186181
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Period 4 sequence [ 2, 2, 3, 2, ...] except a(0) = 1.
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0
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1, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2
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OFFSET
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0,2
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COMMENTS
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Continued fraction expansion of sqrt(33)/4. - Bruno Berselli, Feb 14 2011
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LINKS
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FORMULA
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Euler transform of length 4 sequence [ 2, 0, -2, 1].
Moebius transform is length 4 sequence [ 2, 1, 0, -1].
a(n) = 2 * b(n) where b() is multiplicative with b(2) = 3/2, b(2^e) = 1 if e>1, b(p^e) = 1 if p>2.
G.f.: (1 + x + x^2)^2 / (1 - x^4). a(-n) = a(n). a(4*n + 2) = 3, a(2*n + 1) = 2, a(4*n) = 2 except a(0) = 1.
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EXAMPLE
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1 + 2*x + 3*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 2*x^7 + 2*x^8 + 2*x^9 + ...
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MATHEMATICA
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PROG
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(PARI) {a(n) = 2 - (n==0) + (n%4 == 2)}
(PARI) {a(n) = polcoeff( (1 + x + x^2)^2 / (1 - x^4) + x * O(x^abs(n)), abs(n))}
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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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