OFFSET
0,2
COMMENTS
4*a(n) is the total number of holes in a certain box fractal (start with 8 boxes, 0 hole) after n iterations. See illustration in link. - Kival Ngaokrajang, Jan 27 2015
LINKS
Kival Ngaokrajang, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (11, -26, 16).
FORMULA
a(n) = (4*8^(n+1) - 7*2^(n+1) + 3)/21. - Mitch Harris, Jun 27 2005 - corrected by Yahia Kahloune, May 06 2013
a(0) = 1, a(n) = 8*a(n-1) + 2^(n+1) - 1. - Vincenzo Librandi, Feb 09 2011
MAPLE
a:=n->sum((8^(n-j)-2^(n-j))/6, j=0..n): seq(a(n), n=1..19); # Zerinvary Lajos, Jan 15 2007
PROG
(PARI) Vec(1/((1-x)*(1-2*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved