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 A322052 Number of decimal strings of length n that contain a specific string xy where x and y are distinct digits. 4
 0, 1, 20, 299, 3970, 49401, 590040, 6850999, 77919950, 872348501, 9645565060, 105583302099, 1146187455930, 12356291257201, 132416725116080, 1411810959903599, 14985692873919910, 158445117779295501, 1669465484919035100, 17536209731411055499, 183692631829191519890, 1919390108560504143401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS See A004189 for the number that do not contain the specified string. LINKS Robert Israel, Table of n, a(n) for n = 1..999 Index entries for linear recurrences with constant coefficients, signature (20,-101,10). FORMULA G.f.: x^2/((1-10*x)*(1-10*x+x^2)). EXAMPLE Suppose the desired string is 03. At length 2 that is the only possibility. At length 3 there are 20 strings that contain it: 03d and d03, where d is any digit. MAPLE f:= gfun:-rectoproc({10*a(n) - 101*a(n + 1) + 20*a(n + 2) - a(n + 3), a(0) = 0, a(1) = 0, a(2) = 1}, a(n), remember): map(f, [\$1..40]); # Robert Israel, Mar 27 2020 CROSSREFS Cf. A004189, A322053, A322054. Partial sums of A322628. Sequence in context: A069326 A001708 A016255 * A250014 A291256 A250015 Adjacent sequences: A322049 A322050 A322051 * A322053 A322054 A322055 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Dec 21 2018 STATUS approved

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Last modified May 31 04:44 EDT 2023. Contains 363061 sequences. (Running on oeis4.)