A090581 - OEIS

%I #8 Dec 07 2016 10:36:06

%S 1,6,21,56,126,252,462,792,1287,2001,2992,4317,6027,8162,10746,13782,

%T 17247,21087,25212,29496,33787,37917,41712,45002,47631,49467,50412,

%U 50412,49467,47631,45002,41712,37917,33787,29496,25212,21087,17247,13782,10746,8162,6027,4317,2992,2001,1287,792,462,252,126,56,21,6,1

%N Number of numbers with 6 decimal digits and sum of digits = n.

%C There are 900000 6-digit numbers, the smallest being 100000 and the largest 999999.

%F G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^5. - _Michael De Vlieger_, Dec 07 2016

%e a(2)=6: 100001, 100010, 100100, 101000, 110000, 200000.

%t Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^#, {x, 0, 9 (# + 1)}], x] &@ 5 (* or *)

%t Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 5 (* _Michael De Vlieger_, Dec 07 2016 *)

%o (PARI) b=vector(54,i,0);for(n=100000,999999,a=eval(Vec(Str(n)));b[sum(j=1,6,a[j])]++);for(n=1,54,print1(b[n],",")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006

%Y Cf. A071817 3-digit numbers, A090579 4-digit numbers, A090580 5-digit numbers.

%K base,fini,full,nonn

%O 1,2

%A _Hugo Pfoertner_, Jan 12 2004