A053655 a(n) = (10^n - 1)*(10^(2*n-1) - 1)/81.

1, 1221, 1233321, 1234444321, 1234555554321, 1234566666654321, 1234567777777654321, 1234567888888887654321, 1234567899999999987654321, 1234567901111111110987654321, 1234567901222222222220987654321, 1234567901233333333333320987654321

Offset

1,2

References

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

Links

Colin Barker, Table of n, a(n) for n = 1..334

Index entries for linear recurrences with constant coefficients, signature (1111,-112110,1111000,-1000000).

Formula

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

Example

a(2) = 11*111 = 1221;
a(3) = 111*11111 = 1233321;
a(4) = 1111*1111111 = 1234444321.

Mathematica

Table[(10^n -1)*(10^(2*n-1) -1)/81, {n, 1, 20}] (* G. C. Greubel, May 18 2019 *)
LinearRecurrence[{1111, -112110, 1111000, -1000000}, {1, 1221, 1233321, 1234444321}, 20] (* Harvey P. Dale, Mar 18 2023 *)

Prog

(PARI) a(n)=(10^n-1)*(10^(2*n-1)-1)/81 \\ Charles R Greathouse IV, Jun 10 2013
(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
(Magma) [(10^n -1)*(10^(2*n-1) -1)/81: n in [1..20]]; // G. C. Greubel, May 18 2019
(Sage) [(10^n -1)*(10^(2*n-1) -1)/81 for n in (1..20)] # G. C. Greubel, May 18 2019
(GAP) List([1..20], n-> (10^n -1)*(10^(2*n-1) -1)/81 ) # G. C. Greubel, May 18 2019

Crossrefs

Sequence in context: A015279 A179140 A091790 * A068262 A328991 A223118

Adjacent sequences: A053652 A053653 A053654 * A053656 A053657 A053658

Keyword

easy,nonn

Author

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

Status

approved