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A322054 Number of decimal strings of length n that do not contain a specific string xx (where x is a single digit). 2
10, 99, 981, 9720, 96309, 954261, 9455130, 93684519, 928256841, 9197472240, 91131561729, 902961305721, 8946835807050, 88648174014939, 878355088397901, 8703029361715560, 86232460051021149, 854419404714630381, 8465866782890863770 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A322053 for the number that do contain the specified string.

LINKS

Table of n, a(n) for n=1..19.

FORMULA

G.f. = x*(10+9*x)/(1-9*x-9*x^2).

a(n) = 9*a(n-1)+9*a(n-2) for n >= 3.

EXAMPLE

Suppose the string is 00. At length 2 there are 99 strings that do not contain it. At length 3 there are 19 strings that do not contain it, 000, 00x, and x00, where x is any nonzero digit. So a(3) = 1000-19 = 981.

CROSSREFS

Cf. A322052, A004189, A322053.

Suggested by A322628.

Sequence in context: A081109 A242633 A004189 * A179558 A179556 A179477

Adjacent sequences:  A322051 A322052 A322053 * A322055 A322056 A322057

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Dec 21 2018

STATUS

approved

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Last modified July 22 14:33 EDT 2019. Contains 325222 sequences. (Running on oeis4.)