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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

%I #30 Jul 31 2021 17:46:15

%S 0,1,20,299,3970,49401,590040,6850999,77919950,872348501,9645565060,

%T 105583302099,1146187455930,12356291257201,132416725116080,

%U 1411810959903599,14985692873919910,158445117779295501,1669465484919035100,17536209731411055499,183692631829191519890,1919390108560504143401

%N Number of decimal strings of length n that contain a specific string xy where x and y are distinct digits.

%C See A004189 for the number that do not contain the specified string.

%H Robert Israel, <a href="/A322052/b322052.txt">Table of n, a(n) for n = 1..999</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20,-101,10).

%F G.f.: x^2/((1-10*x)*(1-10*x+x^2)).

%e 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.

%p 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):

%p map(f, [$1..40]); # _Robert Israel_, Mar 27 2020

%Y Cf. A004189, A322053, A322054.

%Y Partial sums of A322628.

%K nonn,base

%O 1,3

%A _N. J. A. Sloane_, Dec 21 2018

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)