cp's OEIS Frontend

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

%I A167403 #19 Aug 18 2018 19:58:56
%S A167403 1,3,10,35,126,462,1716,6435,24310,92368,352595,1351142,5194385,
%T A167403 20024980,77384340,299671971,1162635441,4518099300,17583582225,
%U A167403 68522664400,267350823015,1044243559263,4082760176300,15977236602150,62576817828876,245279492151021
%N A167403 Number of decimal numbers having n or fewer digits and having the sum of their digits equal to n.
%C A167403 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.
%H A167403 Alois P. Heinz, <a href="/A167403/b167403.txt">Table of n, a(n) for n = 1..1665</a>
%F A167403 a(n) = [x^n] ((x^10-1)/(x-1))^n.
%p A167403 b:= proc(n, i) option remember;
%p A167403       `if`(n=0, 1, `if`(i=0, 0,
%p A167403        add(b(n-j, i-1), j=0..min(n, 9)) ))
%p A167403     end:
%p A167403 a:= n-> b(n, n):
%p A167403 seq(a(n), n=1..30);
%Y A167403 Cf. A130835, A001700.
%Y A167403 Column k=9 of A305161.
%K A167403 base,easy,nonn
%O A167403 1,2
%A A167403 _Alois P. Heinz_, Nov 02 2009