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A130835
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Sum of all numbers having n or fewer digits and having the sum of their digits equal to n.
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5
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1, 33, 1110, 38885, 1399986, 51333282, 1906666476, 71499999285, 2701111108410, 102631111100848, 3917722222183045, 150126888888738762, 5771538888888311735, 222499777777775552780, 8598259999999991401740, 332968856666666633369781, 12918171566666666537484951
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (10^n-1)/9 * [x^n] ((x^10-1)/(x-1))^n. - Alois P. Heinz, Feb 07 2012
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EXAMPLE
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Take n = 3. The numbers to be summed are 111, 3, 30, 300, 210, 201, 120, 102, 21 and 12, which add to 1110.
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MAPLE
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A007953 := proc(n) add(i, i=convert(n, base, 10)) ; end: A130835 := proc(n) local a, i; a := 0 ; for i from 1 to 10^n-1 do if A007953(i) = n then a := a+i ; fi ; od ; RETURN(a) ; end: seq(A130835(n), n=1..4) ; # R. J. Mathar, Aug 01 2007
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 9))))
end:
a:= n-> b(n, n)*(10^n-1)/9:
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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