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

Author

Daniel Mondot, Dec 02 2016

Keywords

• base
• fini
• full
• nonn
• easy

Comments

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

Examples

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

Crossrefs

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

Programs

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 *)

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], ", "))

Formula

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