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%I #23 Nov 03 2015 04:32:16
%S 0,0,2,0,6,10,0,42,86,0,342,682,0,2730,5462,0,21846,43690,0,174762,
%T 349526,0,1398102,2796202,0,11184810,22369622,0,89478486,178956970,0,
%U 715827882,1431655766,0,5726623062,11453246122,0,45812984490,91625968982,0
%N Generalized multiplicative Jacobsthal sequence.
%C 2^n = A087462(n) + A087463(n) + a(n) provides a decomposition of Pascal's triangle.
%H Colin Barker, <a href="/A087464/b087464.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)=2, 1, 0) * C(n, k)}.
%F a(n) = (2/9)*(2^n-3*0^n+2*(-1)^n)*(1-cos(2*Pi*n/3)).
%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.: 2*x^2*(2*x^3-3*x^2-1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).
%F (End)
%t LinearRecurrence[{0,0,7,0,0,8},{0,0,2,0,6,10},40] (* _Harvey P. Dale_, Aug 31 2015 *)
%o (PARI) concat(vector(2), Vec(2*x^2*(2*x^3-3*x^2-1)/((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)) + O(x^100))) \\ _Colin Barker_, Nov 02 2015
%Y Cf. A001045, A087462, A087463.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Sep 08 2003
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