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A335843 a(n) is the number of n-digit positive integers with exactly two distinct base 10 digits. 5
0, 81, 243, 567, 1215, 2511, 5103, 10287, 20655, 41391, 82863, 165807, 331695, 663471, 1327023, 2654127, 5308335, 10616751, 21233583, 42467247, 84934575, 169869231, 339738543, 679477167, 1358954415, 2717908911, 5435817903, 10871635887, 21743271855, 43486543791 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the number of n-digit numbers in A031955.

LINKS

Stefano Spezia, Table of n, a(n) for n = 1..3300

Puzzle Critic, Twitter post about the case n = 5, Jul 16 2020.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Index entries for sequences related to digits.

FORMULA

O.g.f.: 81*x^2/(1 - 3*x + 2*x^2).

E.g.f.: 81*(exp(x) - 1)^2/2.

a(n) = 3*a(n-1) - 2*a(n-2) for n > 2.

a(n) = 81*(2^(n-1) - 1).

a(n) = 81*A000225(n-1).

EXAMPLE

a(1) = 0 since the positive integers must have at least two digits;

a(2) = 81 since #[99] - #[9] - #(11*[9]) = 99 - 9 - 9 = 81;

a(3) = 243 since #[999] - #[99] - #(111*[9]) - #{xyz in N | x,y,z are three different digits with x != 0} = 999 - 99 - 9 - 9*9*8 = 243;

...

MATHEMATICA

LinearRecurrence[{3, -2}, {0, 81}, 31]

PROG

(PARI) concat([0], Vec(81*x^2/(1-3*x+2*x^2)+O(x^31)))

CROSSREFS

Cf. A000225, A031955, A337127, A337313.

Cf. A055642, A235154, A235690, A235717.

Sequence in context: A184068 A211690 A205055 * A255625 A205048 A008876

Adjacent sequences:  A335840 A335841 A335842 * A335844 A335845 A335846

KEYWORD

nonn,easy,base

AUTHOR

Stefano Spezia, Jul 18 2020

EXTENSIONS

a(0) removed by Stefano Spezia, Sep 23 2020

STATUS

approved

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Last modified June 18 16:38 EDT 2021. Contains 345120 sequences. (Running on oeis4.)