%I A140428
%S A140428 0,1,1,3,5,9,15,27,49,91,169,317,599,1143,2197,4251,8269,16161,31711,
%T A140428 62435,123273,243963,483745,960725,1910503,3803295,7577933,15109499,
%U A140428 30143973,60166553,120136687,239955563,479396897,957961755,1914577241
%N A140428 a(n)=A000045(n)+A113405(n).
%C A140428 The inverse binomial transform yields the sequence (-1)^(n+1)*a(n). This 
               property is inherited from the A000045 and A113405 sequences, which 
               have the same property individually. The same sign flipping behavior 
               under inverse binomial transform is found in A001045 and for the 
               sequence with two zeros followed by A000975.
%C A140428 This is often, but not here, related to the recurrences a(n)=2a(n-1)+a(n-2)-2a(n-3) 
               associated with denominators 1-2x-x^2+2x^3=(x-1)(2x-1)(x+1) in the 
               o.g.f., which transform into the similar -(x-1)(2x+1)/(1+x)^4 under 
               the inverse binomial transform, see A137241.
%F A140428 O.g.f.: x(1-2x-3x^4+x^2)/((1-x-x^2)(2x-1)(1+x)(x^2-x+1)). - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Jul 10 2008
%F A140428 a(n)= -A128834(n)/3+2^n/9+A000045(n)-(-1)^n/9. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 10 2008
%e A140428 a(n) and the repeated differences in the followup rows are:
%e A140428 0, 1, 1, 3, 5, 9, 15,..
%e A140428 1, 0, 2, 2, 4, 6, 12,..
%e A140428 -1, 2, 0, 2, 2, 6, 10,..
%e A140428 3, -2, 2, 0, 4, 4, 10,..
%e A140428 -5, 4, -2, 4, 0, 6, 6,..
%e A140428 9, -6, 6, -4, 6, 0, 12,..
%e A140428 -15, 12, -10, 10, -6, -12, 0,..
%e A140428 The main diagonal contains zeros.
%Y A140428 Sequence in context: A018436 A018298 A017913 this_sequence A027154 A052007 
               A117480
%Y A140428 Adjacent sequences: A140425 A140426 A140427 this_sequence A140429 A140430 
               A140431
%K A140428 nonn
%O A140428 0,4
%A A140428 Paul Curtz (bpcrtz(AT)free.fr), Jun 19 2008
%E A140428 Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 
               10 2008