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A099942
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Start with 1, then alternately double or add 2.
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1
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1, 2, 4, 8, 10, 20, 22, 44, 46, 92, 94, 188, 190, 380, 382, 764, 766, 1532, 1534, 3068, 3070, 6140, 6142, 12284, 12286, 24572, 24574, 49148, 49150, 98300, 98302, 196604, 196606, 393212, 393214, 786428, 786430, 1572860, 1572862, 3145724, 3145726
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OFFSET
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0,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2).
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FORMULA
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a(0)=1; for n > 0, a(n) = a(n-1)*(1 + n mod 2) + 2*((n+1) mod 2).
G.f.: (2*x^3 + x^2 + 2*x + 1)/(2*x^4 - 3*x^2 + 1).
3*2^ceiling(n/2) + (-1)^n - 3. - Ralf Stephan, Dec 04 2004
a(2*n) = A033484(n).
a(n-1) + a(n) = A061776(n) for n > 0.
E.g.f.: -2*cosh(x) + 3*cosh(sqrt(2)*x) - 4*sinh(x) + 3*sqrt(2)*sinh(sqrt(2)*x). - Franck Maminirina Ramaharo, Nov 08 2018
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MATHEMATICA
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LinearRecurrence[{0, 3, 0, -2}, {1, 2, 4, 8}, 50] (* Harvey P. Dale, May 03 2016 *)
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PROG
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(PARI) print1(a=1, ", "); for(n=1, 20, print1(a=2*a, ", ", a=a+2, ", "))
(MAGMA) [3*2^Ceiling(n/2) + (-1)^n - 3: n in [0..50]]; // Vincenzo Librandi, Aug 17 2011
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CROSSREFS
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Cf. A033484, A061776, A075427, A083416.
Sequence in context: A287266 A306719 A185400 * A033092 A177909 A259386
Adjacent sequences: A099939 A099940 A099941 * A099943 A099944 A099945
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Nov 12 2004
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EXTENSIONS
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Edited and extended by Klaus Brockhaus, Nov 13 2004
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STATUS
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approved
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