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

0,2

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

Links

Table of n, a(n) for n=0..36.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A213651.

Sequence in context: A352208 A341193 A090579 * A000292 A352669 A101552

Adjacent sequences: A276640 A276641 A276642 * A276644 A276645 A276646

Keyword

nonn,fini,full,base

Author

Antonio Sánchez Chinchón, May 02 2017

Status

approved