A099942 Start with 1, then alternately double or add 2.
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
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2).
Programs
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Magma
[3*2^Ceiling(n/2) + (-1)^n - 3: n in [0..50]]; // Vincenzo Librandi, Aug 17 2011
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Mathematica
LinearRecurrence[{0,3,0,-2},{1,2,4,8},50] (* Harvey P. Dale, May 03 2016 *) -
PARI
print1(a=1,",");for(n=1,20,print1(a=2*a,",",a=a+2,","))
Formula
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
Extensions
Edited and extended by Klaus Brockhaus, Nov 13 2004