login
a(n) = n*5^n + 1.
3

%I #22 Jan 15 2023 09:52:39

%S 1,6,51,376,2501,15626,93751,546876,3125001,17578126,97656251,

%T 537109376,2929687501,15869140626,85449218751,457763671876,

%U 2441406250001,12969970703126,68664550781251,362396240234376,1907348632812501

%N a(n) = n*5^n + 1.

%H Vincenzo Librandi, <a href="/A050916/b050916.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 (11,-35,25).

%F a(n) = 11*a(n-1) - 35*a(n-2) + 25*a(n-3); a(0)=1, a(1)=6, a(2)=51. [_Harvey P. Dale_, Sep 15 2011]

%F G.f.: -(20*x^2-5*x+1)/((x-1)*(5*x-1)^2). [_Colin Barker_, Oct 14 2012]

%t Table[n 5^n+1,{n,0,20}] (* or *) LinearRecurrence[{11,-35,25},{1,6,51},20] (* _Harvey P. Dale_, Sep 15 2011 *)

%o (Magma) [ n*5^n+1: n in [0..20]]; // _Vincenzo Librandi_, Sep 16 2011

%Y Cf. A002064.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 30 1999