A205088 - OEIS

%I #26 Feb 18 2025 17:38:49

%S 11,181,1881,18881,188881,1888881,18888881,188888881,1888888881,

%T 18888888881,188888888881,1888888888881,18888888888881,

%U 188888888888881,1888888888888881,18888888888888881,188888888888888881,1888888888888888881,18888888888888888881

%N a(n) = n 8's sandwiched between two 1's.

%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) + 71.

%F a(n) = (1/9)*(17*10^(n+1) - 71). - _Alexander R. Povolotsky_, Jan 25 2012

%F From _Elmo R. Oliveira_, Feb 18 2025: (Start)

%F G.f.: (11 + 60*x)/((1 - x)*(1 - 10*x)).

%F E.g.f.: exp(x)*(170*exp(9*x) - 71)/9.

%F a(n) = 11*a(n-1) - 10*a(n-2). (End)

%t a[0]=11; a[n_] := a[n-1]*10+71; Table[a[n], {n,0,44}]

%t Table[FromDigits[Join[{1},PadRight[{},n,8],{1}]],{n,0,20}] (* _Harvey P. Dale_, Apr 15 2012 *)

%o (PARI) a(n)=(170*10^n-71)/9 \\ _Charles R Greathouse IV_, Jan 23 2012

%Y Cf. A002282.

%K nonn,easy,less,base

%O 0,1

%A _José María Grau Ribas_, Jan 22 2012