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A228778 a(n) = 2^Fibonacci(n) + 1. 0
2, 3, 3, 5, 9, 33, 257, 8193, 2097153, 17179869185, 36028797018963969, 618970019642690137449562113, 22300745198530623141535718272648361505980417, 13803492693581127574869511724554050904902217944340773110325048447598593 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n+2) = a(n+1)*a(n) - a(n) - a(n+1) + 2, a(0)=2, a(1)=3.

Binet type formula: log_2(a(n)-1) = (1/sqrt(5)) * (r^n - s^n), where r and s are the roots of x^2-x-1. (this is true by definition).

a(n) = A000301(n) + 1 = A063896(n) + 2. - Alois P. Heinz, Aug 12 2017

MAPLE

a:= n-> 1 + 2^(<<0|1>, <1|1>>^n)[1, 2]:

seq(a(n), n=0..15);  # Alois P. Heinz, Aug 12 2017

MATHEMATICA

Table[2^Fibonacci[n] + 1, {n, 0, 13}] (* T. D. Noe, Sep 07 2013 *)

CROSSREFS

Cf. A000045, A000301, A063896.

Sequence in context: A241741 A175147 A001180 * A296674 A297073 A019460

Adjacent sequences:  A228775 A228776 A228777 * A228779 A228780 A228781

KEYWORD

nonn

AUTHOR

Yeshwant Shivrai Valaulikar and M. Tamba, Sep 04 2013

STATUS

approved

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Last modified May 8 19:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)