OFFSET
0,2
COMMENTS
a(n) is also the total number of holes in a variation of a box fractal as in illustration. - Kival Ngaokrajang, May 23 2014 [As observed by Hans Havermann, this seems to be incorrect: e.g., for n = 2 the illustration shows 28 small holes plus two larger holes. - M. F. Hasler, Oct 05 2020]
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..200
Kival Ngaokrajang, Illustration for n = 1..4
Index entries for linear recurrences with constant coefficients, signature (11,-10).
FORMULA
From Vincenzo Librandi, Jul 22 2010: (Start)
a(n) = a(n-1) + 2*10^(n-1) with a(0) = 0.
a(n) = 11*a(n-1) - 10*a(n-2) with a(0) = 0, a(1) = 2. (End)
G.f.: 2*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Feb 24 2017
E.g.f.: 2*exp(x)*(exp(9*x) - 1)/9. - Stefano Spezia, Sep 13 2023
MATHEMATICA
LinearRecurrence[{11, -10}, {0, 2}, 50] (* Jinyuan Wang, Feb 27 2020 *)
PROG
(Maxima) A002276(n):=2*(10^n - 1)/9$
makelist(A002276(n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */
(PARI) a(n)=10^n\9*2 \\ M. F. Hasler, Mar 27 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved