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%I #29 Apr 09 2020 11:03:51
%S 0,0,0,1,6,24,81,250,732,2073,5742,15664,42273,113202,301428,799273,
%T 2112774,5571816,14668209,38563882,101285580,265817145,697214430,
%U 1827923296,4790749761,12552714594,32884171236,86133353545,225582998262,590749858968,1546935014097
%N a(n) = Fibonacci(2*n)-2^n+1.
%H Colin Barker, <a href="/A047790/b047790.txt">Table of n, a(n) for n = 0..1000</a>
%H T. Mansour and A. O. Munagi, <a href="https://doi.org/10.1016/j.ejc.2009.07.001">Block-connected set partitions</a>, European J. Combin., 31 (2010), 887-902, Table 3 column 3.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,9,-2).
%F a(0)=0, a(1)=0, a(2)=0, a(3)=1, a(n)=6*a(n-1)-12*a(n-2)+ 9*a(n-3)- 2*a(n-4). - _Harvey P. Dale_, Jan 19 2012
%F G.f.: x^3/(1 - 6*x + 12*x^2 - 9*x^3 + 2*x^4). - _Benedict W. J. Irwin_, Nov 02 2016
%F a(n) = (1-2^n-((3-sqrt(5))/2)^n/sqrt(5)+((3+sqrt(5))/2)^n/sqrt(5)). - _Colin Barker_, Nov 02 2016
%p with(combstruct): SeqSeqSeqL := [T, {T=Sequence(S, card > 1), S=Sequence(U, card > 1), U=Sequence(Z, card >0)}, unlabeled]: seq(count(SeqSeqSeqL, size=j+1), j=0..29); # _Zerinvary Lajos_, Apr 16 2009
%t Table[Fibonacci[2n]-2^n+1,{n,0,30}] (* or *) LinearRecurrence[ {6,-12,9,-2},{0,0,0,1},30] (* _Harvey P. Dale_, Jan 19 2012 *)
%t CoefficientList[Series[x^3/(1 - 6 x + 12 x^2 - 9 x^3 + 2 x^4), {x, 0, 30}], x] (* _Benedict W. J. Irwin_, Nov 02 2016 *)
%o (Sage) [lucas_number1(n,3,1)-lucas_number1(n,3,2) for n in range(0,30)] # _Zerinvary Lajos_, Jul 06 2008
%o (PARI) concat(vector(3), Vec(x^3/(1-6*x+12*x^2-9*x^3+2*x^4) + O(x^40))) \\ _Colin Barker_, Nov 02 2016
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_
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