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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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2
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1, 33, 1110, 38885, 1399986, 51333282, 1906666476, 71499999285, 2701111108410, 102631111100848, 3917722222183045, 150126888888738762, 5771538888888311735, 222499777777775552780, 8598259999999991401740, 332968856666666633369781, 12918171566666666537484951
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..190
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FORMULA
| 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
| 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
| 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
b:= proc(n, i) option remember; if n<0 or i<0 then 0 elif i=0 then `if` (n=0, 1, 0) elif n=0 then 1 else add (b(n-k, i-1), k=0..9) fi end: a:= n-> b(n, n) *(10^n-1) /9: seq (a(n), n=1..20); # Alois P. Heinz, Nov 02 2009
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CROSSREFS
| Cf. A167403.
Sequence in context: A189199 A009977 A187539 * A077420 A158688 A065424
Adjacent sequences: A130832 A130833 A130834 * A130836 A130837 A130838
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KEYWORD
| base,nonn,changed
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AUTHOR
| J. M. Bergot (thekingfishb(AT)yahoo.ca), Jul 18 2007
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EXTENSIONS
| a(4)-a(6) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 01 2007
a(7)-a(12) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jul 02 2009
More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 02 2009
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