

A097581


a(n) = 3*2^floor((n1)/2) + (1)^n.


3



2, 4, 5, 7, 11, 13, 23, 25, 47, 49, 95, 97, 191, 193, 383, 385, 767, 769, 1535, 1537, 3071, 3073, 6143, 6145, 12287, 12289, 24575, 24577, 49151, 49153, 98303, 98305, 196607, 196609, 393215, 393217, 786431, 786433, 1572863, 1572865
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OFFSET

1,1


COMMENTS

Previous name was: a(1)=2 then if n even a(n)=a(n1)+2 and if n odd a(n)=a(n2)+a(n1)1.
This sequence a(n)=A016116(n1)+A086341(n). Generalization: starting with a(1) even then if n even a(n)=a(n1)+2 and if n odd a(n)=a(n2)+a(n1)1 you get a new sequence as a(1) increases. But if a(1) is odd, you get always the same sequence with only less values as a(1) increases. If a(1) is even, the sequence difference between two sequences with different but consecutive a(1) is the sequence of powers of 2 = 2,2,4,4,8,8,16,16,32,32,......


LINKS



FORMULA

a(n) = a(n1) + 2*a(n2) + 2*a(n3).
G.f.: x*(2+6*x+5*x^2)/((1+x)*(12*x^2)). (End)


EXAMPLE

Starting with a(1)=4 the new sequence is 4,6,9,11,19,21,39,41,79,81,159,161
The sequence difference between sequence starting with a(1)=4 and the sequence starting with a(1)=2 is 2,2,4,4,8,8,16,16,32,32,64,64,.......


MATHEMATICA

LinearRecurrence[{1, 2, 2}, {2, 4, 5}, 40] (* Harvey P. Dale, Aug 10 2011 *)
Table[3*2^(Floor[(n  1)/2]) + (1)^n, {n, 1, 50}] (* G. C. Greubel, Apr 18 2017 *)


PROG

(PARI) a(n)=3*2^floor((n1)/2)+(1)^n


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

Equation in the comment corrected by R. J. Mathar, Nov 13 2009


STATUS

approved



