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a(n) = (10^n-1)*(91/81)-n*10^n/9.
2

%I #16 Mar 18 2024 09:33:21

%S 9,89,789,6789,56789,456789,3456789,23456789,123456789,123456789,

%T -9876543211,-209876543211,-3209876543211,-43209876543211,

%U -543209876543211,-6543209876543211,-76543209876543211,-876543209876543211,-9876543209876543211

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

%H Harry J. Smith, <a href="/A064616/b064616.txt">Table of n, a(n) for n=1..150</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-120,100).

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

%F 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

%t LinearRecurrence[{21,-120,100},{9,89,789},20] (* _Harvey P. Dale_, May 15 2022 *)

%o (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

%o (PARI) Vec(x*(100*x-9)/((x-1)*(10*x-1)^2) + O(x^100)) \\ _Colin Barker_, Sep 15 2014

%Y Cf. A002275, A014925, A064617.

%K base,easy,sign

%O 1,1

%A _Henry Bottomley_, Sep 26 2001