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

0,2

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).

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

Mathematica

LinearRecurrence[{0, 3, 0, -2}, {1, 2, 4, 8}, 50] (* Harvey P. Dale, May 03 2016 *)

Prog

(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

Crossrefs

Cf. A033484, A061776, A075427, A083416.

Sequence in context: A287266 A306719 A185400 * A033092 A177909 A259386

Adjacent sequences: A099939 A099940 A099941 * A099943 A099944 A099945

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 12 2004

Extensions

Edited and extended by Klaus Brockhaus, Nov 13 2004

Status

approved