%I A084128
%S A084128 1,2,12,56,272,1312,6336,30592,147712,713216,3443712,16627712,80285696,
%T A084128 387653632,1871757312,9037643776,43637604352,210700992512,1017354387456,
%U A084128 4912221519872,23718303629312,114522100596736,552961616904192
%N A084128 Generalized Fibonacci sequence.
%C A084128 Binomial transform of A084058.
%H A084128 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A084128 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A084128 G.f.: (1-2x)/(1-4x-4x^2). E.g.f.: exp(2x)cosh(2sqrt(2)x). a(n)=4a(n-1)+4a(n-2), 
               a(0)=1, a(1)=2; a(n)=(2+2sqrt(2))^n/2 + (2-2sqrt(2))^n/2;
%o A084128 (PARI) a(n)=if(n<0,0,polsym(4+4*x-x^2,n)[n+1]/2)
%o A084128 (Other) sage: [lucas_number2(n,4,-4)/2 for n in xrange(0, 23)]# [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
%Y A084128 Cf. A057087, A001541.
%Y A084128 Equals 2^n * A001333(n).
%Y A084128 Sequence in context: A020522 A037130 A078543 this_sequence A044047 A105487 
               A098453
%Y A084128 Adjacent sequences: A084125 A084126 A084127 this_sequence A084129 A084130 
               A084131
%K A084128 easy,nonn
%O A084128 0,2
%A A084128 Paul Barry (pbarry(AT)wit.ie), May 16 2003