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%I #27 Dec 25 2021 09:05:56
%S 1,1,2,7,25,85,277,877,2725,8365,25477,77197,233125,702445,2113477,
%T 6352717,19082725,57297325,171990277,516167437,1548895525,4647473005,
%U 13943991877,41835121357,125511655525,376547549485,1129667814277,3389053774477,10167261986725
%N a(0)=a(1)=1, a(2)=2; thereafter a(n) = 3*a(n-1) + 3*2^(n-3) - 2.
%H Vincenzo Librandi, <a href="/A169651/b169651.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6). - _R. J. Mathar_, Apr 20 2010
%F G.f.: (1 - 5*x + 7*x^2 - x^4)/((1-x)*(1-2*x)*(1-3*x)). [corrected by _Georg Fischer_, May 11 2019]
%F a(n) = 4*3^(n-2) - 3*2^(n-2) + 1, n>1. - _R. J. Mathar_, Apr 20 2010
%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(0)=1, a(1)=1, a(2)=2, a(3)=7, a(4)=25. - _Harvey P. Dale_, Nov 23 2011
%F E.g.f.: (11 + 36*exp(x) - 27*exp(2*x) + 16*exp(3*x) + 6*x)/36. - _Stefano Spezia_, Dec 24 2021
%p a:=n->if n <= 1 then 1 elif n=2 then 2 else 3*a(n-1)+3*2^(n-3)-2; fi;
%t Join[{1,1},RecurrenceTable[{a[2]==2,a[n]==3a[n-1]+3 2^(n-3)-2},a, {n,30}]] (* or *) Join[{1,1},LinearRecurrence[{6,-11,6},{2,7,25},30]](* _Harvey P. Dale_, Nov 23 2011 *)
%Y Arises in analyzing A169648.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Apr 07 2010
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