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

Author

N. J. A. Sloane, Nov 12 2004

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A033484, A061776, A075427, A083416.

Programs

Magma

[3*2^Ceiling(n/2) + (-1)^n - 3: n in [0..50]]; // Vincenzo Librandi, Aug 17 2011

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