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A032020
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Number of compositions (ordered partitions) of n into distinct parts.
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17
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1, 1, 1, 3, 3, 5, 11, 13, 19, 27, 57, 65, 101, 133, 193, 351, 435, 617, 851, 1177, 1555, 2751, 3297, 4757, 6293, 8761, 11305, 15603, 24315, 30461, 41867, 55741, 74875, 98043, 130809, 168425, 257405, 315973, 431065, 558327, 751491, 958265, 1277867
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n)= the number of different ways to run up a staircase with n steps, taking steps of distinct sizes where the order matters and there is no other restriction on the number or the size of each step taken. - Mohammad K. Azarian (azarian(AT)evansville.edu), May 21 2008
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REFERENCES
| B. Richmond and A. Knopfmacher, Compositions with distinct parts, Aequationes Mathematicae 49 (1995), pp. 86-97.
Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem II, Missouri Journal of Mathematical Sciences, Vol. 16, No. 1, Winter 2004, pp. 12-17.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
C. G. Bower, Transforms (2)
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FORMULA
| "AGK" (ordered, elements, unlabeled) transform of 1, 1, 1, 1...
G.f.: Sum(k >= 0; k! x^((k^2+k)/2) / Prod(1<=j<=k; 1-x^j)) - David W. Wilson (davidwwilson(AT)comcast.net) May 04 2000
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EXAMPLE
| a(6) = 11 because 6 = 5+1 = 4+2 = 3+2+1 = 3+1+2 = 2+4 = 2+3+1 = 2+1+3 = 1+5 = 1+3+2 = 1+2+3
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MATHEMATICA
| f[list_]:=Length[list]!; Table[Total[Map[f, Select[IntegerPartitions[n], Sort[#] == Union[#] &]]], {n, 0, 30}]
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CROSSREFS
| Cf. A003242, A032011.
Sequence in context: A100886 A072337 A132751 * A084656 A073749 A201866
Adjacent sequences: A032017 A032018 A032019 * A032021 A032022 A032023
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Apr 01 1998
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