A229135 - OEIS

%I #27 Sep 08 2022 08:46:05

%S 0,4,20,102,520,2570,12300,57358,262160,1179666,5242900,23068694,

%T 100663320,436207642,1879048220,8053063710,34359738400,146028888098,

%U 618475290660,2611340116006,10995116277800,46179488366634,193514046488620,809240558043182,3377699720527920

%N n * (2 + 2^(2*n - 1)).

%C a(n) mod 9 is periodic: repeat 0, 4, 2, 3, 7, 5, 6, 1, 8.

%C b(n) = a(n) - n = 0, 3, 18, 99, 516, 2565, 12294,... = A215149(2n)/2.

%H Vincenzo Librandi, <a href="/A229135/b229135.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-33,40,-16).

%F a(n) = n + A215149(2n)/2.

%F a(n) = (A228827(n) - A000367(n))/A002445(n).

%F a(n) = 2*n*A123166(n).

%F G.f.: (34*x^3 - 20*x^2 + 4*x)/((1-x)^2*(1-4*x)^2). - _Ralf Stephan_, Sep 20 2013

%e 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 Table[(n (2 + 2^(2 n - 1))), {n, 0, 40}] (* _Vincenzo Librandi_, Sep 20 2013 *)

%o (PARI) a(n) = n*(2+2^(2*n-1)); \\ _Michel Marcus_, Sep 16 2013

%o (Magma) [n*(2 + 2^(2*n - 1)): n in [0..30]]; // _Vincenzo Librandi_, Sep 20 2013

%Y Cf. A005843, A052539, A081294, A215149, A228827, A000367, A002445, A123166.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Sep 15 2013

%E Better definition by Michel Marcus.

%E More terms from _Vincenzo Librandi_, Sep 20 2013