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Search: id:A098101
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| A098101 |
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Number of partitions of 2n for which the square of the largest part equals the sum of the squares of the other parts. |
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+0
1
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| 1, 1, 2, 2, 2, 5, 4, 7, 11, 12, 15, 29, 31, 45, 67, 77, 105, 161, 187, 260, 352, 431, 577, 801, 950, 1279, 1676, 2074, 2706, 3514, 4287, 5596, 7128, 8782
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OFFSET
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1,3
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COMMENT
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There are no such partitions of 2n+1.
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EXAMPLE
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For n=6 the five partitions {6,6}, {5,4,3}, {4,3,2,1,1,1}, {4,2,2,2,2} and {3,1,1,1,1,1,1,1,1,1} and no others, satisfy the stated requirements, so a(12)=5.
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MATHEMATICA
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(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{p = Partitions[n], l = PartitionsP[n], c = 0, k = 2}, While[k < l + 1, If[ p[[k, 1]]^2 == Plus @@ (Drop[p[[k]], 1]^2), c++ ]; k++ ]; c]; Table[ f[n], {n, 67}] (from Robert G. Wilson v Sep 23 2004)
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CROSSREFS
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Sequence in context: A134634 A103286 A058704 this_sequence A105960 A081290 A168256
Adjacent sequences: A098098 A098099 A098100 this_sequence A098102 A098103 A098104
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Sep 22 2004
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EXTENSIONS
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More terms from Robert G. Wilson v Sep 23 2004
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