A064616 a(n) = (10^n-1)*(91/81)-n*10^n/9.

9, 89, 789, 6789, 56789, 456789, 3456789, 23456789, 123456789, 123456789, -9876543211, -209876543211, -3209876543211, -43209876543211, -543209876543211, -6543209876543211, -76543209876543211, -876543209876543211, -9876543209876543211

Offset: 1

Author

Henry Bottomley, Sep 26 2001

Keywords

• base
• easy
• sign

Links

• Harry J. Smith, Table of n, a(n) for n=1..150
• Index entries for linear recurrences with constant coefficients, signature (21,-120,100).

Crossrefs

Cf. A002275, A014925, A064617.

Programs

Mathematica

LinearRecurrence[{21,-120,100},{9,89,789},20] (* Harvey P. Dale, May 15 2022 *)

PARI

{ a=0; q=1; for (n=1, 150, a+=(10 - n)*q; q*=10; write("b064616.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 20 2009

PARI

Vec(x*(100*x-9)/((x-1)*(10*x-1)^2) + O(x^100)) \\ Colin Barker, Sep 15 2014

Formula

a(n) = a(n-1)+(10-n)*10^(n-1) = (19-n)*A002275(n)-A064617(n) = 10*A002275(n)-A014925(n).

a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). G.f.: x*(100*x-9) / ((x-1)*(10*x-1)^2). - Colin Barker, Sep 15 2014