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
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).
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
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)