A278971 Number of 8-digit numbers whose sum of digits is n.

1, 8, 36, 120, 330, 792, 1716, 3432, 6435, 11439, 19433, 31732, 50016, 76350, 113178, 163284, 229713, 315645, 424215, 558279, 720147, 911304, 1132140, 1381710, 1657545, 1955535, 2269905, 2593305, 2917035, 3231405, 3526195, 3791180, 4016685, 4194135, 4316565, 4379055, 4379055, 4316565, 4194135, 4016685, 3791180, 3526195, 3231405, 2917035, 2593305, 2269905, 1955535, 1657545, 1381710, 1132140, 911304, 720147, 558279, 424215, 315645, 229713, 163284, 113178, 76350, 50016, 31732, 19433, 11439, 6435, 3432, 1716, 792, 330, 120, 36, 8, 1

Offset

1,2

Comments

There are 90000000 numbers with 8 decimal digits, the smallest being 10000000 and the largest 99999999.

Links

Table of n, a(n) for n=1..72.

Formula

G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^7. - Michael De Vlieger, Dec 07 2016

Example

a(2)=8: 10000001, 10000010, 10000100, 10001000, 10010000, 10100000, 11000000, 20000000.

Mathematica

Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^#, {x, 0, 9 (# + 1)}], x] &@ 7 (* Michael De Vlieger, Dec 07 2016 *)

Prog

(PARI) b=vector(72, i, 0); for(n=10000000, 99999999, a=eval(Vec(Str(n))); b[sum(j=1, 8, a[j])]++); for(n=1, 72, print1(b[n], ", "))

Crossrefs

Cf. A071817 (3-digit numbers), A090579 (4-digit numbers), A090580 (5-digit numbers), A090581 (6-digit numbers), A278969 (7-digit numbers).

Sequence in context: A008490 A023033 A341205 * A000580 A290995 A229888

Adjacent sequences: A278968 A278969 A278970 * A278972 A278973 A278974

Keyword

base,fini,full,nonn,easy

Author

Daniel Mondot, Dec 02 2016

Status

approved