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%I #14 Sep 08 2022 08:45:24
%S 1,14,33,130,341,1134,3193,10010,29181,89254,264353,799890,2386021,
%T 7185374,21501513,64613770,193622861,581305494,1743042673,5230875650,
%U 15689131701,47074385614,141209175833,423655489530,1270910544541
%N a(n) = Sum_{j=1..n} (3^j + (-2)^j).
%C First primes are a(11)=264353 and a(17)=193622861. More primes?
%C Additional primes: a(71), a(91), a(431). - _Harvey P. Dale_, Jan 24 2013
%H Harvey P. Dale, <a href="/A116150/b116150.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,5,-6).
%F a(n) = (9*3^n + 4*(-2)^n - 13)/6.
%F From _G. C. Greubel_, May 10 2019: (Start)
%F a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3).
%F G.f.: x*(1 + 12*x)/((1-x)*(1+2*x)*(1-3*x)).
%F E.g.f.: (4*exp(-2*x) - 13*exp(x) + 9*exp(3*x))/6.
%t Accumulate[Table[3^i+(-2)^i,{i,30}]] (* _Harvey P. Dale_, Jan 24 2013 *)
%o (PARI) {a(n) = (9*3^n + 4*(-2)^n - 13)/6}; \\ _G. C. Greubel_, May 10 2019
%o (Magma) [(9*3^n + 4*(-2)^n - 13)/6: n in [1..30]]; // _G. C. Greubel_, May 10 2019
%o (Sage) [(9*3^n + 4*(-2)^n - 13)/6 for n in (1..30)] # _G. C. Greubel_, May 10 2019
%o (GAP) List([1..30], n-> (9*3^n + 4*(-2)^n - 13)/6) # _G. C. Greubel_, May 10 2019
%K nonn
%O 1,2
%A _Zak Seidov_, Apr 14 2007
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