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%I #5 Nov 12 2023 13:31:23
%S 0,9,139,1419,12079,92859,669319,4617699,30878959,201792939,
%T 1295974999,8212422579,51499341439,320287850619,1978857202279,
%U 12161478061059,74421280021519,453832688077899,2759692966903159,16742329188365139,101377580843991199,612894508749226779,3700556151386869639
%N a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 5.
%C a(n) is the number of n-digit numbers in A366962.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-74,120).
%F a(n) = 29*6^(n-1) - 49*5^(n-1) + 5*4^n.
%F a(n) = 15*a(n-1) - 74*a(n-2) + 120*a(n-3) for n > 3.
%F O.g.f.: x^2*(9 + 4*x)/((1 - 4*x)*(1 - 5*x)*(1 - 6*x)).
%F E.g.f.: (145*exp(6*x) - 294*exp(5*x) + 150*exp(4*x) - 1)/30.
%t LinearRecurrence[{15,-74,120},{0,9,139},23]
%Y Cf. A366962.
%Y Cf. A000302, A000351, A000400.
%Y Cf. A367243, A367244, A367245, A367247, A367248, A367249, A367250.
%K nonn,base,easy
%O 1,2
%A _Stefano Spezia_, Nov 11 2023
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