A083446 a(n) = ((10^n - 1) - 9^n)/9.

2, 30, 382, 4550, 52062, 579670, 6328142, 68064390, 723690622, 7624326710, 79730051502, 828681574630, 8569245282782, 88234318656150, 905219979016462, 9258090922259270, 94433929411444542, 961016475814111990

Offset

2,1

Comments

Let k(n) be the largest n-digit number, 10^n - 1, and let m(n) be the product of its digits, 9^n; then a(n) = (k(n) - m(n))/9.

Links

Matthew House, Table of n, a(n) for n = 2..996

Index entries for linear recurrences with constant coefficients, signature (20,-109,90).

Formula

G.f.: 2*x^2*(1-5*x)/((1-x)*(1-9*x)*(1-10*x)).

a(n) = 20*a(n-1) - 109*a(n-2) + 90*a(n-3). - Matthew House, Jan 16 2017

Example

a(4) = (9999 - 9*9*9*9)/9 = 382.

Mathematica

LinearRecurrence[{20, -109, 90}, {2, 30, 382}, 20] (* Harvey P. Dale, Oct 12 2017 *)

Prog

(PARI) for (n=2, 30, print1(((10^n -1) - 9^n)/9, ", "))

Crossrefs

Cf. A083445.

Sequence in context: A230610 A231597 A216119 * A230726 A091345 A147682

Adjacent sequences: A083443 A083444 A083445 * A083447 A083448 A083449

Keyword

base,easy,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 01 2003

Extensions

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 15 2004

Edited by Jon E. Schoenfield, Jan 16 2017

Status

approved