A167403 Number of decimal numbers having n or fewer digits and having the sum of their digits equal to n.

1, 3, 10, 35, 126, 462, 1716, 6435, 24310, 92368, 352595, 1351142, 5194385, 20024980, 77384340, 299671971, 1162635441, 4518099300, 17583582225, 68522664400, 267350823015, 1044243559263, 4082760176300, 15977236602150, 62576817828876, 245279492151021

Offset: 1

Author

Alois P. Heinz, Nov 02 2009

Keywords

• base
• easy
• nonn

Comments

a(3) = 10, because 10 decimal numbers have 3 or fewer digits and a digit sum of 3: 3, 30, 300, 12, 120, 201, 21, 210, 102, 111.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1665

Crossrefs

Cf. A130835, A001700.

Column k=9 of A305161.

Programs

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, `if`(i=0, 0,
       add(b(n-j, i-1), j=0..min(n, 9)) ))
    end:
a:= n-> b(n, n):
seq(a(n), n=1..30);

Formula

a(n) = [x^n] ((x^10-1)/(x-1))^n.