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A117298
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Number of partitions of n with unique smallest part and unique largest part.
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0
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1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 15, 21, 25, 34, 42, 55, 67, 88, 106, 137, 166, 210, 254, 320, 384, 478, 575, 708, 848, 1039, 1239, 1507, 1795, 2167, 2574, 3094, 3661, 4378, 5171, 6153, 7246, 8591, 10088, 11914, 13960, 16424, 19197, 22519, 26253, 30701, 35718
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(2*n+1)= A002865(2*n+1)+1, a(2*n)= A002865(2*n).
a(n) = A117995(n)+1.
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MATHEMATICA
| (* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{p = Partitions@n, q = PartitionsP@n, c = 0, k = 1}, While[k < q, s = Split@ p[[k]]; If[Length@First@s == 1 && Length@Last@s == 1, c++ ]; k++ ]; c]; Array[f, 51] (* Robert G. Wilson v *)
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CROSSREFS
| Sequence in context: A061287 A064651 A094991 * A018052 A018124 A124745
Adjacent sequences: A117295 A117296 A117297 * A117299 A117300 A117301
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KEYWORD
| easy,nonn
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AUTHOR
| Emeric Deutsch and Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 23 2006
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Apr 25 2006
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