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a(n) = (4*n - 3) * 2^(n - 1).
4

%I #16 Sep 16 2022 20:45:15

%S 1,10,36,104,272,672,1600,3712,8448,18944,41984,92160,200704,434176,

%T 933888,1998848,4259840,9043968,19136512,40370176,84934656,178257920,

%U 373293056,780140544,1627389952,3388997632,7046430720,14629732352,30333206528,62813896704

%N a(n) = (4*n - 3) * 2^(n - 1).

%C Central terms of the triangle in A118413.

%H Vincenzo Librandi, <a href="/A118415/b118415.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).

%F a(n) = A016813(n-1)*A000079(n-1).

%F O.g.f.: x*(1+6*x)/(-1+2*x)^2 . - _R. J. Mathar_, Feb 26 2008

%t CoefficientList[Series[(1 + 6 x)/(-1 + 2 x)^2, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 21 2014 *)

%t LinearRecurrence[{4,-4},{1,10},30] (* _Harvey P. Dale_, Sep 16 2022 *)

%o (Magma)[(4*n-3)*2^(n-1): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2010

%Y Cf. A058962.

%K nonn,easy

%O 1,2

%A _Reinhard Zumkeller_, Apr 27 2006

%E More terms from _R. J. Mathar_, Feb 26 2008