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A066723
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Number of distinct partitions of n-th triangular number which can be obtained by merging parts in the partition 1+2+...+n.
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1
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1, 1, 2, 5, 13, 36, 109, 340, 1116, 3744, 12981, 45722, 165247, 603242, 2242932
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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EXAMPLE
| For n=4, the 13 partitions are 10, 1+9, 2+8, 3+7, 4+6, 5+5, 1+2+7, 1+3+6, 1+4+5, 2+3+5, 2+4+4, 3+3+4, 1+2+3+4. 3+7 and 4+6 can be obtained in two ways each: 3+7 = (3)+(1+2+4) = (1+2)+(3+4), 4+6 = (4)+(1+2+3) = (1+3)+(2+4).
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MATHEMATICA
| addto[ p_, k_ ] := Module[ {}, lth=Length[ p ]; Union[ Sort/@Append[ Table[ Join[ Take[ p, i-1 ], {p[ [ i ] ]+k}, Take[ p, i-lth ] ], {i, 1, lth} ], Append[ p, k ] ] ] ]; addtolist[ plist_, k_ ] := Union[ Join@@(addto[ #, k ]&/@plist) ]; l[ 0 ]={{}}; l[ n_ ] := l[ n ]=addtolist[ l[ n-1 ], n ]; a[ n_ ] := Length[ l[ n ] ]
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CROSSREFS
| Cf. A000217, A066740.
Sequence in context: A135337 A133365 A135335 * A000994 A148296 A148297
Adjacent sequences: A066720 A066721 A066722 * A066724 A066725 A066726
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KEYWORD
| more,nonn
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AUTHOR
| Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jan 15 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 18 2002
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