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A167403
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Number of decimal 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, 3, 10, 35, 126, 462, 1716, 6435, 24310, 92368, 352595, 1351142, 5194385, 20024980, 77384340, 299671971, 1162635441, 4518099300, 17583582225, 68522664400, 267350823015, 1044243559263, 4082760176300, 15977236602150, 62576817828876, 245279492151021
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OFFSET
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1,2
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COMMENTS
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a(3) = 10, because 10 decimal numbers have 3 or fewer digits and a digit sum of 3: 3, 30, 300, 12, 120, 201, 21, 210, 102, 111.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..500
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FORMULA
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a(n) = [x^n] ((x^10-1)/(x-1))^n.
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MAPLE
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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):
seq (a(n), n=1..30);
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CROSSREFS
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Cf. A130835, A001700.
Sequence in context: A087946 A122068 A099908 * A001700 A088218 A110556
Adjacent sequences: A167400 A167401 A167402 * A167404 A167405 A167406
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KEYWORD
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base,easy,nonn
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AUTHOR
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Alois P. Heinz, Nov 02 2009
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STATUS
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approved
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