OFFSET
0,2
COMMENTS
a(n) = T(5, n), array T given by A048483.
Sequence is generated by the Northwest (NW) direction of circles put around circle(s). See illustration. - Odimar Fabeny, Aug 09 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Odimar Fabeny, Illustration for this sequence
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
a(n) = 2*a(n-1) + 5, n > 0, a(0) = 1. - Paul Barry, Aug 25 2004
Equals binomial transform of [1, 6, 6, 6, ...]. - Gary W. Adamson, Apr 29 2008
From Colin Barker, Sep 17 2012: (Start)
a(n) = 3*2^(1+n) - 5. a(n) = 3*a(n-1) - 2*a(n-2).
G.f.: (1+4*x)/((1-x)*(1-2*x)). (End)
a(n + 1) = 3 * 2^n - 5 = 1 + 2 * (Sum_{i=0..n-1} 3i) for n > 0. - Gerasimov Sergey and Alonso del Arte, May 03 2014
EXAMPLE
a(2) = 6 * 2^2 - 5 = 6 * 4 - 5 = 24 - 5 = 19.
a(3) = 6 * 2^3 - 5 = 6 * 8 - 5 = 48 - 5 = 43.
MAPLE
MATHEMATICA
6(2^Range[0, 35]) - 5 (* Alonso del Arte, May 03 2014 *)
PROG
(Magma) [6*2^n - 5: n in [0..30]]; // Vincenzo Librandi, May 18 2011
(PARI) a(n)=6*2^n-5 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 11 1999
EXTENSIONS
Simpler definition from Ralf Stephan
STATUS
approved