OFFSET
0,1
COMMENTS
a(n) + a(n-1)^2 = (a(n-1)+1)^2. - Vincenzo Librandi, Mar 24 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
a(n+1) = 2*a(n) + 1.
G.f.: ( 12-11*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 25 2011
EXAMPLE
a(2) = 13*2^2-1 = 51.
MATHEMATICA
Table[13 2^n - 1, {n, 0, 30}] (* Vincenzo Librandi, Mar 24 2013 *)
LinearRecurrence[{3, -2}, {12, 25}, 40] (* Harvey P. Dale, Feb 06 2019 *)
PROG
(BASIC) for j = 0 to 30 : print str$((13*2^j)-1)+", "; : next j
(Magma) [13*2^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 28 2011
(PARI) a(n) = 13*2^n-1; \\ Michel Marcus, Jan 17 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jeremy Gardiner, Oct 23 2011
STATUS
approved