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%I A175162 #22 Oct 13 2024 00:17:44
%S A175162 32,48,80,144,272,528,1040,2064,4112,8208,16400,32784,65552,131088,
%T A175162 262160,524304,1048592,2097168,4194320,8388624,16777232,33554448,
%U A175162 67108880,134217744,268435472,536870928,1073741840,2147483664,4294967312,8589934608,17179869200
%N A175162 a(n) = 16*(2^n + 1).
%H A175162 G. C. Greubel, <a href="/A175162/b175162.txt">Table of n, a(n) for n = 0..1000</a>
%H A175162 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A175162 a(n) = A173786(n+4, 4).
%F A175162 a(n) = 3*a(n-1) - 2*a(n-2), a(0)=32, a(1)=48. - _Vincenzo Librandi_, Dec 28 2010
%F A175162 From _G. C. Greubel_, Jul 08 2021: (Start)
%F A175162 G.f.: 16*(2 - 3*x)/((1-x)*(1-2*x)).
%F A175162 E.g.f.: 16*(exp(2*x) + exp(x)). (End)
%t A175162 16*(2^Range[0,30] +1) (* or *) LinearRecurrence[{3,-2},{32,48},30] (* _Harvey P. Dale_, Jun 08 2017 *)
%o A175162 (Magma) I:=[32,48]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Jul 08 2021
%o A175162 (Sage) [16*(2^n +1) for n in (0..40)] # _G. C. Greubel_, Jul 08 2021
%Y A175162 Sequences of the form m*(2^n + 1): A000051 (m=1), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), A175161 (m=8), this sequence (m=16), A175163 (m=32).
%Y A175162 Cf. A173786.
%K A175162 nonn,easy
%O A175162 0,1
%A A175162 _Reinhard Zumkeller_, Feb 28 2010

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