cp's OEIS Frontend

A048480 a(n) = T(8,n), array T given by A048472.

%I A048480 #24 Aug 28 2025 13:23:27
%S A048480 1,10,37,109,289,721,1729,4033,9217,20737,46081,101377,221185,479233,
%T A048480 1032193,2211841,4718593,10027009,21233665,44826625,94371841,
%U A048480 198180865,415236097,868220929,1811939329,3774873601,7851737089,16307453953,33822867457,70061654017
%N A048480 a(n) = T(8,n), array T given by A048472.
%H A048480 Vincenzo Librandi, <a href="/A048480/b048480.txt">Table of n, a(n) for n = 0..1000</a>
%H A048480 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%F A048480 a(n) = 9*n * 2^(n-1) + 1.
%F A048480 a(0)=1, a(1)=10, a(2)=37, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - _Harvey P. Dale_, Jul 09 2014
%F A048480 G.f.: (1+5*x-5*x^2) / ((1-x)*(1-2*x)^2). - _Colin Barker_, Feb 18 2016
%F A048480 E.g.f.: exp(x)*(1 + 9*exp(x)*x). - _Stefano Spezia_, Aug 28 2025
%t A048480 Table[9*n*2^(n-1)+1,{n,0,30}] (* or *) LinearRecurrence[{5,-8,4},{1,10,37},30] (* _Harvey P. Dale_, Jul 09 2014 *)
%o A048480 (Magma) [9*n * 2^(n-1) + 1: n in [0..30]]; // _Vincenzo Librandi_, Sep 23 2011
%o A048480 (PARI) Vec((1+5*x-5*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Feb 18 2016
%Y A048480 Cf. A008591 (contains n-th difference of a(n),a(n-1),...,a(0)).
%Y A048480 Cf. A048472.
%K A048480 nonn,easy,changed
%O A048480 0,2
%A A048480 _Clark Kimberling_