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A186813
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n/2 times period 4 sequence [ 1, 2, 3, 2, ...].
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1
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0, 1, 3, 3, 2, 5, 9, 7, 4, 9, 15, 11, 6, 13, 21, 15, 8, 17, 27, 19, 10, 21, 33, 23, 12, 25, 39, 27, 14, 29, 45, 31, 16, 33, 51, 35, 18, 37, 57, 39, 20, 41, 63, 43, 22, 45, 69, 47, 24, 49, 75, 51, 26, 53, 81, 55, 28, 57, 87, 59, 30, 61, 93, 63, 32, 65, 99, 67, 34, 69, 105, 71, 36
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..72.
M. Somos, Rational Function Multiplicative Coefficients
Index to sequences with linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1).
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FORMULA
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a(n) is multiplicative with a(2) = 3, a(2^e) = 2^(e-1) if e>1, a(p^e) = p^e if p>2.
Euler transform of length 6 sequence [ 3, -3, 1, 2, 0, -1].
G.f.: x * (1 + x) * (1 + x^3) / ((1 - x) * (1 + x^2))^2. a(-n) = -a(n). a(n) = n/2 * A068073(n).
a(n) = n*(4-i^n-(-i)^n)/4 with i=sqrt(-1) - Bruno Berselli, Mar 10 2011.
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EXAMPLE
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x + 3*x^2 + 3*x^3 + 2*x^4 + 5*x^5 + 9*x^6 + 7*x^7 + 4*x^8 + 9*x^9 + ...
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MATHEMATICA
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CoefficientList[Series[x(1+x)(1+x^3)/((1-x)(1+x^2))^2, {x, 0, 80}], x] (* From Harvey P. Dale, Mar 6 2011 *)
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PROG
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(PARI) {a(n) = n/2 * [ 1, 2, 3, 2][n%4 + 1]}
(PARI) {a(n) = sign(n) * polcoeff( x * (1 + x) * (1 + x^3) / ((1 - x) * (1 + x^2))^2 + x * O(x^abs(n)), abs(n))}
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CROSSREFS
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Cf. A068073.
Cf. A187601. - Bruno Berselli, Mar 12 2011
Sequence in context: A070163 A083343 A186111 * A110898 A147994 A106365
Adjacent sequences: A186810 A186811 A186812 * A186814 A186815 A186816
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KEYWORD
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nonn,mult
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AUTHOR
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Michael Somos, Feb 27 2011
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STATUS
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approved
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