A367248 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 7.
0, 5, 111, 1601, 19095, 204545, 2045511, 19508081, 179752215, 1613908385, 14202967911, 123028446161, 1052237271735, 8907026785025, 74758478722311, 623053865857841, 5162154289325655, 42558224511290465, 349394287423788711, 2858263098464575121, 23311522539676521975
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (21,-146,336).
Crossrefs
Programs
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Mathematica
LinearRecurrence[{21,-146,336},{0,5,111},21]
Formula
a(n) = 23*8^(n-1) - 41*7^(n-1) + 3*6^n.
a(n) = 21*a(n-1) - 146*a(n-2) + 336*a(n-3) for n > 3.
O.g.f.: x^2*(5 + 6*x)/((1 - 6*x)*(1 - 7*x)*(1 - 8*x)).
E.g.f.: (161*exp(8*x) - 328*exp(7*x) + 168*exp(6*x) - 1)/56.
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