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%I #5 Nov 12 2023 13:30:49
%S 0,13,119,733,3815,18133,81599,354493,1504055,6278053,25904879,
%T 106011853,431253095,1746686773,7051884959,28403182813,114200118935,
%U 458563556293,1839545301839,7374058107373,29543870469575,118318410678613,473702458475519,1896096339905533,7588244995073015
%N a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 3.
%C a(n) is the number of n-digit numbers in A366960.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,24).
%F a(n) = 27*4^(n-1) - 41*3^(n-1) + 7*2^n.
%F a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3) for n > 3.
%F O.g.f.: x^2*(13 + 2*x)/((1 - 2*x)*(1 - 3*x)*(1 - 4*x)).
%F E.g.f.: (exp(x) - 1)^2*(81*exp(2*x) - 2*exp(x) - 1)/12.
%t LinearRecurrence[{9,-26,24},{0,13,119},25]
%Y Cf. A366960.
%Y Cf. A000079, A000244, A000302.
%Y Cf. A367243, A367245, A367246, A367247, A367248, A367249, A367250.
%K nonn,base,easy
%O 1,2
%A _Stefano Spezia_, Nov 11 2023
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