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A229135 n * (2 + 2^(2*n - 1)).

%I A229135 #27 Sep 08 2022 08:46:05
%S A229135 0,4,20,102,520,2570,12300,57358,262160,1179666,5242900,23068694,
%T A229135 100663320,436207642,1879048220,8053063710,34359738400,146028888098,
%U A229135 618475290660,2611340116006,10995116277800,46179488366634,193514046488620,809240558043182,3377699720527920
%N A229135 n * (2 + 2^(2*n - 1)).
%C A229135 a(n) mod 9 is periodic: repeat 0, 4, 2, 3, 7, 5, 6, 1, 8.
%C A229135 b(n) = a(n) - n = 0, 3, 18, 99, 516, 2565, 12294,... = A215149(2n)/2.
%H A229135 Vincenzo Librandi, <a href="/A229135/b229135.txt">Table of n, a(n) for n = 0..1000</a>
%H A229135 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-33,40,-16).
%F A229135 a(n) = n + A215149(2n)/2.
%F A229135 a(n) = (A228827(n) - A000367(n))/A002445(n).
%F A229135 a(n) = 2*n*A123166(n).
%F A229135 G.f.: (34*x^3 - 20*x^2 + 4*x)/((1-x)^2*(1-4*x)^2). - _Ralf Stephan_, Sep 20 2013
%e A229135 a(0)=0*(2+1/2)=0, a(1)=1*(2+2)=4, a(2)=2*(2+8)=20, a(3)=3*(2+32)=102, a(4)=4*(2+128)=520, a(5)=5*(2+512)=2570.
%t A229135 Table[(n (2 + 2^(2 n - 1))), {n, 0, 40}] (* _Vincenzo Librandi_, Sep 20 2013 *)
%o A229135 (PARI) a(n) = n*(2+2^(2*n-1)); \\ _Michel Marcus_, Sep 16 2013
%o A229135 (Magma) [n*(2 + 2^(2*n - 1)): n in [0..30]]; // _Vincenzo Librandi_, Sep 20 2013
%Y A229135 Cf. A005843, A052539, A081294, A215149, A228827, A000367, A002445, A123166.
%K A229135 nonn,easy
%O A229135 0,2
%A A229135 _Paul Curtz_, Sep 15 2013
%E A229135 Better definition by Michel Marcus.
%E A229135 More terms from _Vincenzo Librandi_, Sep 20 2013