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A276643 Number of distinct 4-digit vehicle plates whose sum is n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A038409 A201722 A090579 * A000292 A101552 A038419

Adjacent sequences:  A276640 A276641 A276642 * A276644 A276645 A276646

KEYWORD

nonn,fini,full,base,changed

AUTHOR

Antonio Sánchez Chinchón, May 02 2017

STATUS

approved

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Last modified June 28 04:43 EDT 2017. Contains 288813 sequences.