A048500 - OEIS

%I #19 Sep 08 2022 08:44:57

%S 1,2,11,43,135,375,967,2375,5639,13063,29703,66567,147463,323591,

%T 704519,1523719,3276807,7012359,14942215,31719431,67108871,141557767,

%U 297795591,624951303,1308622855,2734686215,5704253447,11878268935,24696061959,51271172103

%N a(n) = 2^(n-1)*(7*n-12)+7.

%H Vincenzo Librandi, <a href="/A048500/b048500.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).

%F a(n) = T(6, n), array T given by A048494.

%F a(0)=1, a(1)=2, a(2)=11, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - _Harvey P. Dale_ and _Vincenzo Librandi_, Sep 23 2011

%F G.f.: (1-3*x+9*x^2) / ((1-x)*(1-2*x)^2). - _Colin Barker_, Aug 24 2016

%o (Magma) [2^(n-1)*(7*n-12)+7: n in [0..30]]; // _Vincenzo Librandi_, Sep 23 2011

%o (PARI) Vec((1-3*x+9*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Aug 24 2016

%Y Cf. A048494.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_

%E Formula from _Ralf Stephan_, Jan 15 2004