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%I #5 Nov 12 2023 13:31:31
%S 0,7,131,1609,16415,150817,1296191,10641169,84520175,654958177,
%T 4980233951,37312922929,276288797135,2026564724737,14750977566911,
%U 106695818055889,767748717541295,5500729672814497,39270143125479071,279511731951144049,1984459091985376655,14059238393314971457
%N a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 6.
%C a(n) is the number of n-digit numbers in A366963.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-107,210).
%F a(n) = 27*7^(n-1) - 47*6^(n-1) + 4*5^n.
%F a(n) = 21*a(n-1) - 146*a(n-2) + 336*a(n-3) for n > 3.
%F O.g.f.: x^2*(7 + 5*x)/((1 - 5*x)*(1 - 6*x)*(1 - 7*x)).
%F E.g.f.: (162*exp(7*x) - 329*exp(6*x) + 168*exp(5*x) - 1)/42.
%t LinearRecurrence[{18,-107,210},{0,7,131},22]
%Y Cf. A366963.
%Y Cf. A000351, A000400, A000420.
%Y Cf. A367243, A367244, A367245, A367246, A367248, A367249, A367250.
%K nonn,base,easy
%O 1,2
%A _Stefano Spezia_, Nov 11 2023