

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
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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^n4^n, ..., 9^n8^n. These also give the number of ndigit 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^(n1)  8*9^(n1).
G.f.: (x*(1  x))/(1  19*x + 90*x^2).  Bobby Milazzo, May 02 2014
a(n) = 19*a(n1)  90*a(n2).  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 twodigit 9ish numbers.


MAPLE

A088924:=n>9*10^(n1)  8*9^(n1); 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^n8*9^n \\ M. F. Hasler, May 04 2015
(MAGMA) [9*10^(n1)  8*9^(n1): 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



