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A367250 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 9.

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%I A367250 #5 Nov 12 2023 13:31:53
%S A367250 0,1,35,703,11231,158311,2062655,25466743,302423471,3487593511,
%T A367250 39314599775,435241463383,4748453693711,51186327429511,
%U A367250 546278900354495,5781325731101623,60750456603203951,634502309615150311,6592506388026870815,68188442304165981463,702543059232886986191
%N A367250 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 9.
%C A367250 a(n) is the number of n-digit numbers in A366966.
%H A367250 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (27,-242,720).
%F A367250 a(n) = 9*10^(n-1) - 17*9^(n-1) + 8^n.
%F A367250 a(n) = 27*a(n-1) - 242*a(n-2) + 720*a(n-3) for n > 3.
%F A367250 O.g.f.: x^2*(1 + 8*x)/((1 - 8*x)*(1 - 9*x)*(1 - 10*x)).
%F A367250 E.g.f.: (81*exp(10*x) - 170*exp(9*x) + 90*exp(8*x) - 1)/90.
%t A367250 LinearRecurrence[{27,-242,720},{0,1,35},21]
%Y A367250 Cf. A366966.
%Y A367250 Cf. A001018, A001019, A011557.
%Y A367250 Cf. A367243, A367244, A367245, A367246, A367247, A367248, A367249.
%K A367250 nonn,base,easy
%O A367250 1,3
%A A367250 _Stefano Spezia_, Nov 11 2023