A276643 Number of distinct 4-digit vehicle plates whose sum is n.

1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 282, 348, 415, 480, 540, 592, 633, 660, 670, 660, 633, 592, 540, 480, 415, 348, 282, 220, 165, 120, 84, 56, 35, 20, 10, 4, 1

Offset: 0

Author

Antonio Sánchez Chinchón, May 02 2017

Keywords

• nonn
• fini
• full
• base

Comments

a(n) is the number of weak compositions (ordered partitions) into four parts 0, 1, 2, ..., 9. - Joerg Arndt, May 02 2017

The 4th row of A213651. - Omar E. Pol, May 02 2017

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

Examples

			a(0) = 1 because 0000 is the only plate which sums to 0.
a(1) = 4 because there are 4 plates which sum to 1: 0001, 0010, 0100 and 1000.
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
		

Crossrefs

Cf. A213651.

Programs

Mathematica

Length /@ Split@ Sort@ Map[Total, IntegerDigits@ Range[0, 10^4 - 1]] (* Michael De Vlieger, May 03 2017 *)

PARI

{ my(x='x+O('x^44)); Vec(sum(k=0,9,x^k)^4) } \\ Joerg Arndt, May 02 2017

R

library(dplyr)
data=expand.grid(0:9, 0:9, 0:9, 0:9, KEEP.OUT.ATTRS = FALSE)
data %>%
  mutate(n=Var1+Var2+Var3+Var4) %>%
  group_by(n) %>%
  summarise(value=n()) -> suc
View(suc)