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%I #8 Jun 13 2015 00:51:14
%S 1,1,3,2,11,21,22,85,171,170,683,1365,1366,5461,10923,10922,43691,
%T 87381,87382,349525,699051,699050,2796203,5592405,5592406,22369621,
%U 44739243,44739242,178956971,357913941,357913942,1431655765,2863311531
%N Generalized Jacobsthal sequence.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,7,0,0,8).
%F a(n)=sum{k=0..n, if (mod(k(n-2k), 3)=0, comb(n, k), 0) }; a(3n)=A001045(3n+1)-A001045(3n); a(3n+1)=A001045(3n+2), a(3n+2)=A001045(3n+3).
%F G.f.: (4x^4-5x^3+3x^2+x+1)/(-8x^6-7x^3+1).
%F G.f.: ( -1-x-3*x^2+5*x^3-4*x^4 ) / ( (2*x-1)*(1+x)*(4*x^2+2*x+1)*(x^2-x+1) ). - _R. J. Mathar_, Dec 10 2014
%Y Cf. A087628.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Sep 14 2003