login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A276643 Number of distinct 4-digit vehicle plates whose sum is n. 0

%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 4-digit 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 16 10:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)