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%I #19 Nov 03 2015 04:32:01
%S 1,1,1,8,5,11,64,43,85,512,341,683,4096,2731,5461,32768,21845,43691,
%T 262144,174763,349525,2097152,1398101,2796203,16777216,11184811,
%U 22369621,134217728,89478485,178956971,1073741824,715827883,1431655765,8589934592,5726623061
%N Generalized mod 3 multiplicative Jacobsthal sequence.
%C 2^n = a(n) + A087463(n) + A087464(n) provides a decomposition of Pascal's triangle.
%C Multiplicative analog of A078008.
%H Colin Barker, <a href="/A087462/b087462.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)=0, 1, 0) * C(n, k).
%F a(n) = 2^n-2/3*(1-cos(2*Pi*n/3))*(A001045(n)+2*A001045(n-1)+0^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.: -(4*x^5-2*x^4+x^3+x^2+x+1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).
%F (End)
%o (PARI) Vec(-(4*x^5-2*x^4+x^3+x^2+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
%Y Cf. A001045, A001018 (trisection), A082311 (trisection), A082365 (trisection).
%K easy,nonn
%O 0,4
%A _Paul Barry_, Sep 08 2003
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