%I A097038
%S A097038 0,1,1,5,7,21,35,85,155,341,651,1365,2667,5461,10795,21845,43435,87381,
%T A097038 174251,349525,698027,1398101,2794155,5592405,11180715,22369621,
%U A097038 44731051,89478485,178940587,357913941,715795115,1431655765,2863245995
%N A097038 A Jacobsthal variant.
%C A097038 Convolution of A001045 and A077957. Also interleaving of A002450(n+1) 
               and A006095(n+1).
%F A097038 G.f. : 1/(1-x-2x^2)-1/(1-2x^2)=x/((1-2x^2)(1-x-2x^2)); a(n)=2*2^n/3+(-1)^n/
               3-2^(n/2)(1+(-1)^n)/2; a(n)=sum{k=0..floor((n+1)/2), binomial(n-k+1, 
               k-1)2^k }; a(n)=sum{k=0..n, 2^(k/2)(1+(-1)^k)A001045(n-k)/2 }; a(n)=A001045(n+1)-A077957(n).
%Y A097038 Sequence in context: A076197 A002596 A098597 this_sequence A049114 A030735 
               A162462
%Y A097038 Adjacent sequences: A097035 A097036 A097037 this_sequence A097039 A097040 
               A097041
%K A097038 easy,nonn
%O A097038 0,4
%A A097038 Paul Barry (pbarry(AT)wit.ie), Jul 19 2004