%I
%S 1,4,10,20,35,56,84,120,165,220,282,348,415,480,540,592,633,660,670,
%T 660,633,592,540,480,415,348,282,220,165,120,84,56,35,20,10,4,1
%N Number of distinct 4digit vehicle plates whose sum is n.
%C a(n) is the number of weak compositions (ordered partitions) into four parts 0, 1, 2, ..., 9.  _Joerg Arndt_, May 02 2017
%C The 4th row of A213651.  _Omar E. Pol_, May 02 2017
%C a(n) is the number of integers in the range 0 to 9999 whose sum of digits = n. There are 10000 numbers in the range 0 to 9999 and in this sequence they are distributed according to the sum of their digits (n).  _Miquel Cerda_, Jun 14 2017
%e a(0) = 1 because 0000 is the only plate which sums to 0.
%e a(1) = 4 because there are 4 plates which sum to 1: 0001, 0010, 0100 and 1000.
%e a(2) = 10 because there are 10 numbers whose digits sum to 2: 2, 11, 20, 101, 110, 200, 1001, 1010, 1100, 2000.  _Miquel Cerda_, Jun 14 2017
%t Length /@ Split@ Sort@ Map[Total, IntegerDigits@ Range[0, 10^4  1]] (* _Michael De Vlieger_, May 03 2017 *)
%o (R)
%o library(dplyr)
%o data=expand.grid(0:9, 0:9, 0:9, 0:9, KEEP.OUT.ATTRS = FALSE)
%o data %>%
%o mutate(n=Var1+Var2+Var3+Var4) %>%
%o group_by(n) %>%
%o summarise(value=n()) > suc
%o View(suc)
%o (PARI) { my(x='x+O('x^44)); Vec(sum(k=0,9,x^k)^4) } \\ _Joerg Arndt_, May 02 2017
%Y Cf. A213651.
%K nonn,fini,full,base
%O 0,2
%A _Antonio Sánchez Chinchón_, May 02 2017
