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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
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
Sequence in context: A272780 A171606 A006914 * A204392 A233677 A200938
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.)