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%I #16 Sep 08 2022 08:45:13
%S 3,8,28,104,400,1568,6208,24704,98560,393728,1573888,6293504,25169920,
%T 100671488,402669568,1610645504,6442516480,25769934848,103079477248,
%U 412317384704,1649268490240,6597071863808,26388283260928
%N Number of occurrences of pattern 1-2 after n iterations of morphism A007413.
%H Vincenzo Librandi, <a href="/A093356/b093356.txt">Table of n, a(n) for n = 1..1000</a>
%H S. Kitaev and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0210170">Counting the occurrences of generalized patterns...</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -8).
%F a(n) = (3*4^(n-1) + 2^n)/2, a(1) = 3.
%F G.f.: (6 - 20*x + 8*x^2)/((1-2*x)*(1-4*x)).
%F a(n) = 6*a(n-1) - 8*a(n-2); a(1)=3, a(2)=8, a(3)=28. -_Harvey P. Dale_, Oct 02 2011
%t Join[{3},Table[(3*4^(n-1)+2^n)/2,{n,2,30}]] (* or *) Join[{3}, LinearRecurrence[ {6,-8},{8,28},30]] (* _Harvey P. Dale_, Oct 02 2011 *)
%o (PARI) a(n)=(3*4^(n-1)+2^n)/2
%o (Magma) [Ceiling((3*(4^(n-1)) + 2^n)/2): n in [1..30]]; // _Vincenzo Librandi_, Oct 03 2011
%K nonn
%O 1,1
%A _Ralf Stephan_, Apr 27 2004
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