A093357 - OEIS

%I #11 May 03 2024 14:16:00

%S 0,4,20,88,368,1504,6080,24448,98048,392704,1571840,6289408,25161728,

%T 100655104,402636800,1610579968,6442385408,25769672704,103078952960,

%U 412316336128,1649266393088,6597067669504,26388274872320

%N Number of occurrences of pattern 2-1 after n iterations of morphism A007413.

%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(1) = 0, a(n) = (3*4^(n-1) - 2^n)/2.

%F G.f.: 4*x*(1-x)/((1-2*x)*(1-4*x)).

%F a(1)=0, a(2)=4, a(3)=20, a(n)=6*a(n-1)-8*a(n-2). - _Harvey P. Dale_, Apr 04 2012

%F a(n) = 4*A010036(n-2). - _R. J. Mathar_, Apr 07 2022

%t Join[{0},Table[(3*4^(n-1)-2^n)/2,{n,2,30}]] (* or *) Join[{0}, LinearRecurrence[{6,-8},{4,20},30]] (* _Harvey P. Dale_, Apr 04 2012 *)

%o (PARI) a(n)=if(n==1,0,(3*4^(n-1)-2^n)/2)

%Y Cf. A007413, A010036.

%K nonn,easy

%O 1,2

%A _Ralf Stephan_, Apr 27 2004