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Search: id:A071976
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| A071976 |
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Lists of length n from {0..9} summing to n but not beginning with 0. |
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+0
4
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| 1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48619, 184735, 705222, 2702609, 10390940, 40062132, 154830696, 599641425, 2326640877, 9042327525, 35194002709, 137160956815, 535193552973, 2090558951396, 8174176541450, 31990402045260
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of n-digit numbers with digit sum n.
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FORMULA
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Equals binomial(2n-2, n-1) for n <= 9, by the stars and bars argument. [To get such a number take n boxes in which the left-most box contains a 1 and the rest are empty. Distribute the remaining n-1 1's into the n boxes subject to the constraint that no box contains more than 9 1's. This can be done in binomial(2n-2, n-1) ways for n <= 9.]
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EXAMPLE
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a(3) = 6 as there are six three-digit numbers with digit sum 3: 102, 111, 120, 201, 210, 300.
a(10) = binomial(18,9)-1; a(11) = binomial(20,10)-21; a(12) = binomial(22,11)-210.
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MATHEMATICA
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Do[c = 0; k = 10^n; l = 10^(n + 1) - 1; While[k < l, If[ Plus @@ IntegerDigits[k] == n + 1, c++ ]; k++ ]; Print[c], {n, 0, 7}]
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PROGRAM
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(PARI) a(n)=local(y=(x^10-1)/(x-1)); if(n<1, 0, polcoeff((y-1)*y^(n-1), n))
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CROSSREFS
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Different from A000984.
Sequence in context: A087944 A056616 A065346 this_sequence A000984 A087433 A119373
Adjacent sequences: A071973 A071974 A071975 this_sequence A071977 A071978 A071979
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KEYWORD
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nonn,base
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 18 2002
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 20, 2002.
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 21 2002
More terms from John W. Layman (layman(AT)math.vt.edu), Jun 22 2002
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