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A088924 Number of "9ish numbers" with n digits. 7
1, 18, 252, 3168, 37512, 427608, 4748472, 51736248, 555626232, 5900636088, 62105724792, 648951523128, 6740563708152, 69665073373368, 716985660360312, 7352870943242808, 75175838489185272, 766582546402667448 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First difference of A016189. ("9" can be replaced by any other nonzero digit, however only the 9ish numbers are closed under lunar multiplication.)

See A257285 - A257289 for first differences of 5^n-4^n, ..., 9^n-8^n. These also give the number of n-digit numbers whose largest digit is 5, 6, 7, 8, respectively. - M. F. Hasler, May 04 2015

LINKS

Table of n, a(n) for n=1..18.

D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

Index entries for sequences related to dismal (or lunar) arithmetic

Index entries for linear recurrences with constant coefficients, signature (19,-90).

FORMULA

a(n) = 9*10^(n-1) - 8*9^(n-1).

G.f.: (x*(1 - x))/(1 - 19*x + 90*x^2). - Bobby Milazzo, May 02 2014

a(n) = 19*a(n-1) - 90*a(n-2). - Vincenzo Librandi, May 04 2015

EXAMPLE

a(2) = 18 because 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 and 99 are the eighteen two-digit 9ish numbers.

MAPLE

A088924:=n->9*10^(n-1) - 8*9^(n-1); seq(A088924(n), n=1..30); # Wesley Ivan Hurt, May 15 2014

MATHEMATICA

Series[(x (1 - x))/(1 - 19 x + 90 x^2), {x, 0, 10}] (* Bobby Milazzo, May 02 2014 *)

Table[9*10^(n - 1) - 8*9^(n - 1), {n, 30}] (* Wesley Ivan Hurt, May 15 2014 *)

PROG

(PARI) a(n)=9*10^n-8*9^n \\ M. F. Hasler, May 04 2015

(MAGMA) [9*10^(n-1) - 8*9^(n-1): n in [1..30]]; // Vincenzo Librandi, May 04 2015

CROSSREFS

Cf. A016189, A011539.

Sequence in context: A060788 A144708 A020528 * A125475 A255371 A016175

Adjacent sequences:  A088921 A088922 A088923 * A088925 A088926 A088927

KEYWORD

base,easy,nonn

AUTHOR

Marc LeBrun, Oct 23 2003

STATUS

approved

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Last modified October 23 11:48 EDT 2019. Contains 328345 sequences. (Running on oeis4.)