This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016203 #33 Mar 26 2025 15:22:49 %S A016203 1,11,95,775,6231,49911,399415,3195575,25565111,204521911,1636177335, %T A016203 13089422775,104715390391,837723139511,6701785148855,53614281256375, %U A016203 428914250182071,3431314001718711,27450512014273975,219604096115240375,1756832768924020151,14054662151396355511 %N A016203 Expansion of g.f. 1/((1-x)*(1-2*x)*(1-8*x)). %C A016203 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 A016203 Kival Ngaokrajang, <a href="/A016203/a016203.pdf">Illustration of initial terms</a> %H A016203 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-26,16). %F A016203 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 A016203 a(0) = 1, a(n) = 8*a(n-1) + 2^(n+1) - 1. - _Vincenzo Librandi_, Feb 09 2011 %F A016203 From _Elmo R. Oliveira_, Mar 26 2025: (Start) %F A016203 E.g.f.: exp(x)*(32*exp(7*x) - 14*exp(x) + 3)/21. %F A016203 a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3). %F A016203 a(n) = A016131(n+1) - A023001(n+2). (End) %p A016203 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 A016203 (PARI) Vec(1/((1-x)*(1-2*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012 %Y A016203 Cf. A016131, A023001. %K A016203 nonn,easy %O A016203 0,2 %A A016203 _N. J. A. Sloane_ %E A016203 More terms from _Elmo R. Oliveira_, Mar 26 2025