cp's OEIS Frontend

A191821 a(n) = n*(2^n - n + 1) + 2^(n-1)*(n^2 - 3*n + 2).

%I A191821 #36 Sep 08 2022 08:45:57
%S A191821 2,6,26,100,332,994,2774,7368,18872,47014,114578,274300,647012,
%T A191821 1507146,3473198,7929616,17956592,40369870,90177194,200277636,
%U A191821 442498652,973078066,2130705926,4647288280,10099883432,21877489014,47244639554,101737037068
%N A191821 a(n) = n*(2^n - n + 1) + 2^(n-1)*(n^2 - 3*n + 2).
%C A191821 Conjecture: generating function = -((2 (-1+6 x-19 x^2+31 x^3-22 x^4+4 x^5))/(1-3 x+2 x^2)^3) - _Harvey P. Dale_, May 10 2021
%H A191821 Vincenzo Librandi, <a href="/A191821/b191821.txt">Table of n, a(n) for n = 1..1000</a>
%H A191821 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-33,63,-66,36,-8).
%F A191821 G.f.: -2*x*(-1 + 6*x - 19*x^2 + 31*x^3 - 22*x^4 + 4*x^5) / ( (2*x-1)^3*(x-1)^3 ). - _R. J. Mathar_, Aug 26 2011
%t A191821 LinearRecurrence[{9,-33,63,-66,36,-8},{2,6,26,100,332,994},50] (* _Vincenzo Librandi_, Nov 25 2011 *)
%t A191821 Table[n(2^n-n+1)+2^(n-1) (n^2-3n+2),{n,30}] (* _Harvey P. Dale_, May 10 2021 *)
%o A191821 (PARI) a(n)=(n^2-n+2)<<(n-1)-n*(n-1) \\ _Charles R Greathouse IV_, Jul 13 2011
%o A191821 (Magma) [n*(2^n-n+1)+2^(n-1)*(n^2-3*n+2): n in [1..40]]; // _Vincenzo Librandi_, Nov 25 2011
%Y A191821 Cf. A188377, A188947, A189890.
%K A191821 nonn,easy
%O A191821 1,1
%A A191821 _Adeniji, Adenike_, Jun 17 2011