A048499 - OEIS

%I #20 Sep 08 2022 08:44:57

%S 1,2,10,38,118,326,838,2054,4870,11270,25606,57350,126982,278534,

%T 606214,1310726,2818054,6029318,12845062,27262982,57671686,121634822,

%U 255852550,536870918,1124073478,2348810246,4898947078,10200547334,21206401030,44023414790

%N a(n) = 2^(n-1)*(6*n-10)+6.

%H Vincenzo Librandi, <a href="/A048499/b048499.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(5, n), array T given by A048494.

%F a(0)=1, a(1)=2, a(2)=10, 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+8*x^2) / ((1-x)*(1-2*x)^2). - _Colin Barker_, Aug 24 2016

%o (Magma) [2^(n-1)*(6*n-10)+6: n in [0..30]]; // _Vincenzo Librandi_, Sep 23 2011

%o (PARI) Vec((1-3*x+8*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