login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A278969 Number of 7-digit numbers whose sum of digits is n. 5
1, 7, 28, 84, 210, 462, 924, 1716, 3003, 5004, 7995, 12306, 18312, 26418, 37038, 50568, 67353, 87648, 111573, 139068, 169863, 203463, 239148, 275988, 312873, 348558, 381723, 411048, 435303, 453438, 464653, 468448, 464653, 453438, 435303, 411048, 381723, 348558, 312873, 275988, 239148, 203463, 169863, 139068, 111573, 87648, 67353, 50568, 37038, 26418, 18312, 12306, 7995, 5004, 3003, 1716, 924, 462, 210, 84, 28, 7, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

There are 9000000 numbers with 7 decimal digits, the smallest being 1000000 and the largest 9999999.

Differs for n >= 10 (5004 vs 5005) from A000579(n+5) = binomial(n+5,6). - M. F. Hasler, Mar 05 2017

LINKS

Table of n, a(n) for n=1..63.

FORMULA

G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^6. - Michael De Vlieger, Dec 07 2016

a(64-n) = a(n), 1 <= n <= 63. - M. F. Hasler, Mar 05 2017

EXAMPLE

a(2)=7: 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 2000000.

MATHEMATICA

Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^#, {x, 0, 9 (# + 1)}], x] &@ 6 (* or *)

Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 6 (* Michael De Vlieger, Dec 07 2016 *)

PROG

(PARI) b=vector(63, i, 0); for(n=1000000, 9999999, a=eval(Vec(Str(n))); b[sum(j=1, 7, a[j])]++); for(n=1, 63, print1(b[n], ", "))

(PARI) Vec((1-x^9)*(1-x^10)^6/(1-x)^7) \\ shorter than (1-x^9)/(1-x)*((1-x^10)/(1-x))^6, but not better. - M. F. Hasler, Mar 05 2017

CROSSREFS

A071817 (3-digit numbers), A090579 (4-digit numbers), A090580 (5-digit numbers), A090581 (6-digit numbers), A278971 (8-digit numbers).

Sequence in context: A049018 A008489 A023032 * A000579 A290994 A049017

Adjacent sequences:  A278966 A278967 A278968 * A278970 A278971 A278972

KEYWORD

base,fini,full,nonn,easy

AUTHOR

Daniel Mondot, Dec 02 2016

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)