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%I #31 Sep 08 2022 08:46:13
%S 2,48,770,11696,175874,2639408,39595010,593936816,8909087234,
%T 133636413488,2004546517250,30068198703536,451022983387394,
%U 6765344759313968,101480171415218690,1522202571304807856,22833038569801700354,342495578547714252848,5137433678217780035330
%N a(n) = (-3 - 28*3^n + 73*15^n)/21.
%C a(n) is the total number of holes at n iterations of a fractal starting with a pattern of 15 boxes and 2 nonsquare holes (see illustration in Links field).
%H Colin Barker, <a href="/A260846/b260846.txt">Table of n, a(n) for n = 0..849</a>
%H Kival Ngaokrajang, <a href="/A260846/a260846.pdf">Illustration of initial terms</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19, -63, 45).
%F a(0) = 2, a(n) = 15*a(n-1) + 2 + 16*3^(n-1) for n > 0.
%F a(n) = 2*15^n + 2*Sum_{i=0..n-1} 15^i*(1 + 8*3^(n-1-i)).
%F G.f.: 2*(8*x^2-5*x-1) / ((x-1)*(3*x-1)*(15*x-1)). - _Colin Barker_, Aug 01 2015
%F a(n) = 19*a(n-1) - 63*a(n-2) + 45*a(n-3) for n>2. - _Colin Barker_, Aug 20 2015
%t Table[(- 3 - 28 3^n + 73 15^n)/21, {n, 0, 20}] (* _Vincenzo Librandi_, Aug 22 2015 *)
%t LinearRecurrence[{19,-63,45},{2,48,770},20] (* _Harvey P. Dale_, Apr 18 2020 *)
%o (PARI) {for (n=0, 100, s=0; for (i=0, n-1, s=s+2*15^i*(1+8*3^(n-1-i))); a=s+2*15^n; print1(a,", "))}
%o (PARI) Vec(2*(8*x^2-5*x-1)/((x-1)*(3*x-1)*(15*x-1)) + O(x^20)) \\ _Colin Barker_, Aug 01 2015
%o (Magma) [(-3-28*3^n+73*15^n)/21: n in [0..25]]; // _Vincenzo Librandi_, Aug 22 2015
%K nonn,easy
%O 0,1
%A _Kival Ngaokrajang_, Aug 01 2015
%E Condensed title by _Colin Barker_, Aug 01 2015
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