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%I #9 Feb 09 2014 17:27:41
%S 1,4,10,20,35,56,84,120,165,219,279,342,405,465,519,564,597,615,615,
%T 597,564,519,465,405,342,279,219,165,120,84,56,35,20,10,4,1
%N Number of numbers with 4 decimal digits and sum of digits = n.
%C There are 9000 numbers with 4 decimal digits, the smallest being 1000 and the largest 9999.
%F G.f.: (x-x^10)/(1-x)*((1-x^10)/(1-x))^3. - _Geoffrey Critzer_, Feb 09 2014
%e a(2)=4: 1001, 1010, 1100, 2000.
%t nn=36;Drop[CoefficientList[Series[(x-x^10)/(1-x)(1-x^10)^3/(1-x)^3,{x,0,nn}],x],1] (* _Geoffrey Critzer_, Feb 09 2014 *)
%o (PARI) b=vector(36,i,0);for(n=1000,9999,a=eval(Vec(Str(n)));b[sum(j=1,4,a[j])]++);for(n=1,36,print1(b[n],",")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006
%Y Cf. A071817 3-digit numbers, A090580 5-digit numbers, A090581 6-digit numbers.
%K base,fini,full,nonn
%O 1,2
%A _Hugo Pfoertner_, Jan 12 2004
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