A294328 a(n) = ((9*n + 8)*10^n - 8)/81.

0, 2, 32, 432, 5432, 65432, 765432, 8765432, 98765432, 1098765432, 12098765432, 132098765432, 1432098765432, 15432098765432, 165432098765432, 1765432098765432, 18765432098765432, 198765432098765432, 2098765432098765432, 22098765432098765432

Offset: 0

Author

Seiichi Manyama, Oct 28 2017

Keywords

• nonn
• easy

Examples

			Curious multiplications:
         2 * 8 =       16;
        32 * 8 =      256;
       432 * 8 =     3456;
      5432 * 8 =    43456;
     65432 * 8 =   523456;
    765432 * 8 =  6123456;
   8765432 * 8 = 70123456.
         2 * 9 =       18;
        32 * 9 =      288;
       432 * 9 =     3888;
      5432 * 9 =    48888;
     65432 * 9 =   588888;
    765432 * 9 =  6888888;
   8765432 * 9 = 78888888.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (21,-120,100).

Crossrefs

Cf. A294327, A294329.

Programs

Mathematica

LinearRecurrence[{21,-120,100},{0,2,32},20] (* Harvey P. Dale, Sep 17 2023 *)

PARI

concat(0, Vec(2*x*(1 - 5*x) / ((1 - x)*(1 - 10*x)^2) + O(x^30))) \\ Colin Barker, Oct 28 2017

Formula

a(n) = (1/9) * A294327(n) = (1/8) * A294329(n).

From Colin Barker, Oct 28 2017: (Start)

G.f.: 2*x*(1 - 5*x) / ((1 - x)*(1 - 10*x)^2).

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

(End)