

A056469


Number of elements in the continued fraction for Sum_{k=0..n} 1/2^2^k.


5



2, 3, 4, 6, 10, 18, 34, 66, 130, 258, 514, 1026, 2050, 4098, 8194, 16386, 32770, 65538, 131074, 262146, 524290, 1048578, 2097154, 4194306, 8388610, 16777218, 33554434, 67108866, 134217730, 268435458, 536870914, 1073741826, 2147483650
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (3,2).


FORMULA

a(0)=2; for n > 0, a(n) = 2^(n1) + 2 = A052548(n1) + 2.
a(n) = floor(2^(n1) + 2).  Vincenzo Librandi, Sep 21 2011
From Colin Barker, Mar 22 2013: (Start)
a(n) = 3*a(n1)  2*a(n2) for n > 2.
G.f.: (x^2+3*x2) / ((x1)*(2*x1)). (End)


MATHEMATICA

LinearRecurrence[{3, 2}, {2, 3, 4}, 40] (* Harvey P. Dale, Apr 23 2015 *)


PROG

(Sage) [floor(gaussian_binomial(n, 1, 2)+3) for n in range(1, 32)] # Zerinvary Lajos, May 31 2009
(Magma) [Floor(2^(n1)+2): n in [0..60]]; // Vincenzo Librandi, Sep 21 2011


CROSSREFS

Cf. A007400. Apart from initial term, same as A052548. See also A089985.
Sequence in context: A106511 A024490 A317200 * A228863 A004047 A355191
Adjacent sequences: A056466 A056467 A056468 * A056470 A056471 A056472


KEYWORD

nonn,easy


AUTHOR

Benoit Cloitre, Dec 07 2002


STATUS

approved



