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 A337313 a(n) is the number of n-digit positive integers with exactly three distinct base 10 digits. 3
 0, 0, 648, 3888, 16200, 58320, 195048, 625968, 1960200, 6045840, 18468648, 56068848, 169533000, 511252560, 1539065448, 4627812528, 13904670600, 41756478480, 125354369448, 376232977008, 1129038669000, 3387795483600, 10164745404648, 30496954122288, 91496298184200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is the number of n-digit numbers in A031962. LINKS Table of n, a(n) for n=1..25. Index entries for linear recurrences with constant coefficients, signature (6,-11,6). Index entries for sequences related to digits. FORMULA O.g.f.: 648*x^3/(1 - 6*x + 11*x^2 - 6*x^3). E.g.f.: 108*(exp(x) - 1)^3. a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 3. a(n) = 648*S2(n, 3) where S2(n, 3) = A000392(n). a(n) = 324*(3^(n-1) - 2^n + 1). a(n) ~ 108 * 3^n. a(n) = 324*(A000244(n-1) - A000225(n)). a(n) = A337127(n, 3). EXAMPLE a(1) = a(2) = 0 since the positive integers must have at least three digits; a(3) = #{xyz in N | x,y,z are three different digits with x != 0} = 9*9*8 = 648; a(4) = 3888 since #[9999] - #[999] - #(1111*[9]) - A335843(4) - #{xywz in N | x,y,w,z are four different digits with x != 0} = 9999 - 999 - 9 - 567 - 9*9*8*7 = 3888; ... MATHEMATICA LinearRecurrence[{6, -11, 6}, {0, 0, 648}, 26] PROG (PARI) concat([0, 0], Vec(648*x^3/(1-6*x+11*x^2-6*x^3)+O(x^26))) CROSSREFS Cf. A000225, A000244, A000392, A031962, A048993, A335843, A337127. Cf. A055642, A180599, A235155, A235691, A235718. Sequence in context: A272780 A171606 A006914 * A204392 A233677 A200938 Adjacent sequences: A337310 A337311 A337312 * A337314 A337315 A337316 KEYWORD nonn,easy,base AUTHOR Stefano Spezia, Aug 22 2020 STATUS approved

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Last modified February 22 16:01 EST 2024. Contains 370256 sequences. (Running on oeis4.)