A053655 - OEIS

%I #20 Mar 18 2023 17:13:42

%S 1,1221,1233321,1234444321,1234555554321,1234566666654321,

%T 1234567777777654321,1234567888888887654321,1234567899999999987654321,

%U 1234567901111111110987654321,1234567901222222222220987654321,1234567901233333333333320987654321

%N a(n) = (10^n - 1)*(10^(2*n-1) - 1)/81.

%D W. Lietzmann, Sonderlinge im Reich der Zahlen, Ferd. Duemmlers Verlag Bonn, 1948, p. 30.

%H Colin Barker, <a href="/A053655/b053655.txt">Table of n, a(n) for n = 1..334</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1111,-112110,1111000,-1000000).

%F G.f.: x*(1 + 110*x - 11100*x^2)/((1-x)*(1-10*x)*(1-100*x)*(1-1000*x)). - _Colin Barker_, Mar 19 2015

%e a(2) = 11*111 = 1221;

%e a(3) = 111*11111 = 1233321;

%e a(4) = 1111*1111111 = 1234444321.

%t Table[(10^n -1)*(10^(2*n-1) -1)/81, {n,1,20}] (* _G. C. Greubel_, May 18 2019 *)

%t LinearRecurrence[{1111,-112110,1111000,-1000000},{1,1221,1233321,1234444321},20] (* _Harvey P. Dale_, Mar 18 2023 *)

%o (PARI) a(n)=(10^n-1)*(10^(2*n-1)-1)/81 \\ _Charles R Greathouse IV_, Jun 10 2013

%o (PARI) Vec(x*(1+110*x-11100*x^2)/((1-x)*(1-10*x)*(1-100*x)*(1-1000*x)) + O(x^20)) \\ _Colin Barker_, Mar 19 2015

%o (Magma) [(10^n -1)*(10^(2*n-1) -1)/81: n in [1..20]]; // _G. C. Greubel_, May 18 2019

%o (Sage) [(10^n -1)*(10^(2*n-1) -1)/81 for n in (1..20)] # _G. C. Greubel_, May 18 2019

%o (GAP) List([1..20], n-> (10^n -1)*(10^(2*n-1) -1)/81 ) # _G. C. Greubel_, May 18 2019

%K easy,nonn

%O 1,2

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 17 2000