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%I #8 Dec 07 2016 10:35:32
%S 1,8,36,120,330,792,1716,3432,6435,11439,19433,31732,50016,76350,
%T 113178,163284,229713,315645,424215,558279,720147,911304,1132140,
%U 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
%N Number of 8-digit numbers whose sum of digits is n.
%C There are 90000000 numbers with 8 decimal digits, the smallest being 10000000 and the largest 99999999.
%F G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^7. - _Michael De Vlieger_, Dec 07 2016
%e a(2)=8: 10000001, 10000010, 10000100, 10001000, 10010000, 10100000, 11000000, 20000000.
%t 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 *)
%o (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], ", "))
%Y Cf. A071817 (3-digit numbers), A090579 (4-digit numbers), A090580 (5-digit numbers), A090581 (6-digit numbers), A278969 (7-digit numbers).
%K base,fini,full,nonn,easy
%O 1,2
%A _Daniel Mondot_, Dec 02 2016
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