A294344 a(n) = ((-9*n + 82)*10^n - 1)/81.

1, 9, 79, 679, 5679, 45679, 345679, 2345679, 12345679, 12345679, -987654321, -20987654321, -320987654321, -4320987654321, -54320987654321, -654320987654321, -7654320987654321, -87654320987654321, -987654320987654321, -10987654320987654321, -120987654320987654321

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (21,-120,100).

Formula

From Colin Barker, Oct 29 2017: (Start)

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

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

(End)

Example

Curious multiplications:
         9 * 8 =       72;
        79 * 8 =      632;
       679 * 8 =     5432;
      5679 * 8 =    45432;
     45679 * 8 =   365432;
    345679 * 8 =  2765432;
   2345679 * 8 = 18765432.
         9 * 9 =       81;
        79 * 9 =      711;
       679 * 9 =     6111;
      5679 * 9 =    51111;
     45679 * 9 =   411111;
    345679 * 9 =  3111111;
   2345679 * 9 = 21111111.

Mathematica

LinearRecurrence[{21, -120, 100}, {1, 9, 79}, 30] (* Harvey P. Dale, Mar 12 2018 *)

Prog

(PARI) Vec((1 - 12*x + 10*x^2) / ((1 - x)*(1 - 10*x)^2) + O(x^30)) \\ Colin Barker, Oct 29 2017

Crossrefs

Cf. A294328.

Sequence in context: A293721 A198857 A126632 * A125909 A125421 A163445

Adjacent sequences: A294341 A294342 A294343 * A294345 A294346 A294347

Keyword

sign,easy

Author

Seiichi Manyama, Oct 28 2017

Status

approved