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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). 4
 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 Robert P. P. McKone, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (9,9). 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. MATHEMATICA T[n_, k_] := LinearRecurrence[{n - 1, n - 1}, {n, n^2 - 1}, k]; T[10, {1, 19}] (* Robert P. P. McKone, Dec 31 2020 *) 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 June 3 09:57 EDT 2023. Contains 363107 sequences. (Running on oeis4.)