login
a(n) = T(5,n), array T given by A048472.
2

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

%S 1,7,25,73,193,481,1153,2689,6145,13825,30721,67585,147457,319489,

%T 688129,1474561,3145729,6684673,14155777,29884417,62914561,132120577,

%U 276824065,578813953,1207959553,2516582401,5234491393,10871635969,22548578305,46707769345

%N a(n) = T(5,n), array T given by A048472.

%C n-th difference of a(n), a(n-1), ..., a(0) is (6, 12, 18, ...).

%H Vincenzo Librandi, <a href="/A048477/b048477.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) = 6*n * 2^(n-1) + 1.

%F G.f.: (1 + 2*x - 2*x^2) / ((1 - x) * (1 - 2*x)^2).

%F a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3) for n>2. - _Colin Barker_, Feb 18 2016

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

%o (PARI) {a(n) = if( n<0, 0, 3 * n * 2^n + 1)}; /* _Michael Somos_, May 13 2014 */

%o (PARI) Vec((1+2*x-2*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Feb 18 2016

%Y Cf. A048472.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_