A016203 Expansion of 1/((1-x)(1-2x)(1-8x)).

1, 11, 95, 775, 6231, 49911, 399415, 3195575, 25565111, 204521911, 1636177335, 13089422775, 104715390391, 837723139511, 6701785148855, 53614281256375, 428914250182071, 3431314001718711, 27450512014273975

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

Table of n, a(n) for n=0..18.

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

Sequence in context: A115203 A164547 A298925 * A241606 A326349 A318599

Adjacent sequences: A016200 A016201 A016202 * A016204 A016205 A016206

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved