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%I #8 Jun 13 2015 00:51:14
%S 1,2,2,2,10,22,22,86,170,170,682,1366,1366,5462,10922,10922,43690,
%T 87382,87382,349526,699050,699050,2796202,5592406,5592406,22369622,
%U 44739242,44739242,178956970,357913942,357913942,1431655766,2863311530
%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-k), 3)=0, comb(n, k), 0) }; a(n)=if (mod(n, 3)=0, A001045(n+1)-A001045(n), A001045(n+1)-(-1)^n).
%F G.f.: ( -1-2*x-2*x^2+5*x^3+4*x^4-8*x^5 ) / ( (2*x-1)*(1+x)*(4*x^2+2*x+1)*(x^2-x+1) ). - _R. J. Mathar_, Dec 10 2014
%Y Cf. A087629.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Sep 14 2003
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