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%I #10 Jul 08 2019 15:53:30
%S 1,5,15,35,70,126,210,330,495,714,992,1330,1725,2170,2654,3162,3675,
%T 4170,4620,4998,5283,5460,5520,5460,5283,4998,4620,4170,3675,3162,
%U 2654,2170,1725,1330,992,714,495,330,210,126,70,35,15,5,1
%N Number of numbers with 5 decimal digits and sum of digits = n.
%C There are 90000 numbers with 5 decimal digits, the smallest being 10000 and the largest 99999.
%F G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^4. - _Michael De Vlieger_, Dec 07 2016
%e a(2)=5: 10001, 10010, 10100, 11000, 20000.
%t Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^4, {x, 0, 45}], x] (* or *)
%t Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 4 (* _Michael De Vlieger_, Dec 07 2016 *)
%t Tally[Total[IntegerDigits[#]]&/@Range[10000,99999]][[All,2]] (* _Harvey P. Dale_, Jul 08 2019 *)
%o (PARI) b=vector(45,i,0);for(n=10000,99999,a=eval(Vec(Str(n)));b[sum(j=1,5,a[j])]++);for(n=1,45,print1(b[n],",")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006
%Y Cf. A071817 3-digit numbers, A090579 4-digit numbers, A090581 6-digit numbers.
%K base,fini,full,nonn
%O 1,2
%A _Hugo Pfoertner_, Jan 12 2004
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