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%I #28 Sep 28 2023 09:45:28
%S 1,11,95,775,6231,49911,399415,3195575,25565111,204521911,1636177335,
%T 13089422775,104715390391,837723139511,6701785148855,53614281256375,
%U 428914250182071,3431314001718711,27450512014273975
%N Expansion of 1/((1-x)(1-2x)(1-8x)).
%C 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
%H Kival Ngaokrajang, <a href="/A016203/a016203.pdf">Illustration of initial terms</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11, -26, 16).
%F a(n) = (4*8^(n+1) - 7*2^(n+1) + 3)/21. - _Mitch Harris_, Jun 27 2005 - corrected by _Yahia Kahloune_, May 06 2013
%F a(0) = 1, a(n) = 8*a(n-1) + 2^(n+1) - 1. - _Vincenzo Librandi_, Feb 09 2011
%p a:=n->sum((8^(n-j)-2^(n-j))/6,j=0..n): seq(a(n), n=1..19); # _Zerinvary Lajos_, Jan 15 2007
%o (PARI) Vec(1/((1-x)*(1-2*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_