A261315 Number of n-digit positive numbers whose digits occur with equal frequency.

9, 90, 657, 4788, 27225, 146619, 544329, 2112084, 3447369, 28995255, 9, 1488185631, 9, 73556822205, 38222232057, 3321970172244, 9, 138479121435807, 9, 2209806802214163, 19711054740199689, 28570005, 9, 15574715941421647071, 141378216540777225, 421224309, 9724427617362202602009

Offset: 1

Author

Robert Israel, Aug 14 2015

Keywords

• nonn
• base

Comments

a(n) is divisible by 9.

a(n) = 9 if n > 10 is prime.

Examples

			For n = 1 there are the numbers 1 to 9.
For n = 2 there are 9 two-digit numbers of the form dd and 81 with two distinct digits, for a total of 90.
For n = 3 there are 9 numbers of the form ddd and 648 with three distinct digits, for a total of 657.
For n = 4 there are 9 numbers of the form dddd, 243 with two distinct digits each occurring twice, and 4536 with four distinct digits, for a total of 4788.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..919

Crossrefs

Cf. A052060.

Programs

Maple

seq(9/10*add(n!/(n/j)!^j * binomial(10,j), j = select(`<=`,numtheory:-divisors(n),10)),n=1..30);

Formula

a(n) = (9/10) * Sum_{j | n, j <= 10} n! * ((n/j)!)^(-j) * binomial(10,j).