A294344 - OEIS

%I #13 Mar 12 2018 16:10:50

%S 1,9,79,679,5679,45679,345679,2345679,12345679,12345679,-987654321,

%T -20987654321,-320987654321,-4320987654321,-54320987654321,

%U -654320987654321,-7654320987654321,-87654320987654321,-987654320987654321,-10987654320987654321,-120987654320987654321

%N a(n) = ((-9*n + 82)*10^n - 1)/81.

%H Colin Barker, <a href="/A294344/b294344.txt">Table of n, a(n) for n = 0..900</a>

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

%F From _Colin Barker_, Oct 29 2017: (Start)

%F G.f.: (1 - 12*x + 10*x^2) / ((1 - x)*(1 - 10*x)^2).

%F a(n) = 21*a(n-1) - 120*a(n-2) + 100*a(n-3) for n>2.

%F (End)

%e Curious multiplications:

%e          9 * 8 =       72;

%e         79 * 8 =      632;

%e        679 * 8 =     5432;

%e       5679 * 8 =    45432;

%e      45679 * 8 =   365432;

%e     345679 * 8 =  2765432;

%e    2345679 * 8 = 18765432.

%e          9 * 9 =       81;

%e         79 * 9 =      711;

%e        679 * 9 =     6111;

%e       5679 * 9 =    51111;

%e      45679 * 9 =   411111;

%e     345679 * 9 =  3111111;

%e    2345679 * 9 = 21111111.

%t LinearRecurrence[{21,-120,100},{1,9,79},30] (* _Harvey P. Dale_, Mar 12 2018 *)

%o (PARI) Vec((1 - 12*x + 10*x^2) / ((1 - x)*(1 - 10*x)^2) + O(x^30)) \\ _Colin Barker_, Oct 29 2017

%Y Cf. A294328.

%K sign,easy

%O 0,2

%A _Seiichi Manyama_, Oct 28 2017