A205085 - OEIS

%I #26 Sep 08 2022 08:46:01

%S 11,151,1551,15551,155551,1555551,15555551,155555551,1555555551,

%T 15555555551,155555555551,1555555555551,15555555555551,

%U 155555555555551,1555555555555551,15555555555555551,155555555555555551,1555555555555555551,15555555555555555551

%N a(n) = n 5's sandwiched between two 1's.

%H Vincenzo Librandi, <a href="/A205085/b205085.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(0)=11, a(n) = 10*a(n-1) + 41.

%F a(n) = (140*10^n - 41)/9 (see PARI code by _Charles R Greathouse IV_).

%F a(n) = 11*a(n-1) - 10*a(n-2). - _Vincenzo Librandi_, Jan 23 2012

%t a[0]=11;a[n_]:=a[n-1]*10+41;Table[a[n],{n,0,44}]

%t LinearRecurrence[{11, -10}, {11, 151}, 50] (* _Vincenzo Librandi_, Jan 23 2012 *)

%t Table[10FromDigits[PadRight[{1},n,5]]+1,{n,20}] (* _Harvey P. Dale_, May 02 2019 *)

%o (PARI) a(n)=(140*10^n-41)/9 \\ _Charles R Greathouse IV_, Jan 23 2012

%o (Magma) I:=[11, 151]; [n le 2 select I[n] else 11*Self(n-1)-10*Self(n-2): n in [1..25]]; // _Vincenzo Librandi_, Jan 23 2012

%K nonn,base,easy,less

%O 0,1

%A _José María Grau Ribas_, Jan 22 2012