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%I #15 Nov 04 2015 11:56:07
%S 0,1,1,0,5,11,0,43,85,0,341,683,0,2731,5461,0,21845,43691,0,174763,
%T 349525,0,1398101,2796203,0,11184811,22369621,0,89478485,178956971,0,
%U 715827883,1431655765,0,5726623061,11453246123,0,45812984491,91625968981,0
%N Generalized multiplicative Jacobsthal sequence.
%C Set A001045(3n)=0 in A001045.
%C 2^n = A087462(n) + a(n) + A087464(n) provides a decomposition of Pascal's triangle.
%H Colin Barker, <a href="/A087463/b087463.txt">Table of n, a(n) for n = 0..1000</a>
%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(n*k, 3)=1, 1, 0)*C(n, k).
%F a(n) = (2/9)*(1-cos(2*Pi*n/3))*(2^n-(-1)^n).
%F From _Colin Barker_, Nov 02 2015: (Start)
%F a(n) = 7*a(n-3)+8*a(n-6) for n>5.
%F G.f.: -x*(4*x^4-2*x^3+x+1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).
%F (End)
%o (PARI) concat(0, Vec(-x*(4*x^4-2*x^3+x+1)/((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)) + O(x^100))) \\ _Colin Barker_, Nov 02 2015
%K easy,nonn
%O 0,5
%A _Paul Barry_, Sep 08 2003
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