OFFSET
1,1
COMMENTS
Extends Euler's 6-term sequence.
In Euler's 6-term sequence we have noticed that e(1) = 2 = 2^0 + 1; e(2) = 3 = 2^1 + 3^0; e(3) = 5 = 2^2 + 1; e(4) = 11 = 2^3 + 3^1; e(5) = 17 = 2^4 + 1; e(6) = 41 = 2^5 + 3^2, which of course immediately leads to our formula above. Note: For m>0, we take m^(1/2) to be the unique positive square root of m.
a(2^n + 1), n=0,1,2,... are the Fermat numbers.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,4,-8,-3,6).
PROG
(PARI) a(n) = 2^(n-1) + (2 + (-1)^n)^((n-2)/2) \\ Charles R Greathouse IV, Jan 29 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ben de la Rosa & Johan Meyer (MeyerJH.sci(AT)mail.uovs.ac.za), Jul 09 2003
EXTENSIONS
More terms from Neven Juric, Apr 10 2008
STATUS
approved