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A090580
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Number of numbers with 5 decimal digits and sum of digits = n.
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8
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1, 5, 15, 35, 70, 126, 210, 330, 495, 714, 992, 1330, 1725, 2170, 2654, 3162, 3675, 4170, 4620, 4998, 5283, 5460, 5520, 5460, 5283, 4998, 4620, 4170, 3675, 3162, 2654, 2170, 1725, 1330, 992, 714, 495, 330, 210, 126, 70, 35, 15, 5, 1
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OFFSET
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1,2
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COMMENTS
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There are 90000 numbers with 5 decimal digits, the smallest being 10000 and the largest 99999.
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LINKS
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FORMULA
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EXAMPLE
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a(2)=5: 10001, 10010, 10100, 11000, 20000.
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MATHEMATICA
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Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^4, {x, 0, 45}], x] (* or *)
Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 4 (* Michael De Vlieger, Dec 07 2016 *)
Tally[Total[IntegerDigits[#]]&/@Range[10000, 99999]][[All, 2]] (* Harvey P. Dale, Jul 08 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,fini,full,nonn
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AUTHOR
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STATUS
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approved
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