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Search: id:A165271
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| A165271 |
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a(n) = p(3*n), where p(n) = number of partitions of n into parts that correspond to areas of distinct pieces of Archimedes' ostomachion. |
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3
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| 1, 2, 5, 9, 17, 27, 43, 64, 90, 124, 163, 211, 261, 321, 381, 446, 511, 576, 638, 694, 746, 786, 818, 836, 844, 836, 818, 786, 746, 694, 638, 576, 511, 446, 381, 321, 261, 211, 163, 124, 90, 64, 43, 27, 17, 9, 5, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The 14 ostomachion pieces and their areas are (following the notation as published in the Bibliotheca Augustana website):
11 triangles: NCO=3, KHT=3, EFQ=6, GCQ=6, BKH=6, ZLF=6, GNC=9, EQG=12, ALZ=12, ABM=12, and BML=12,
2 tetragons: FQCZ=12 and DOCZ=24, and 1 pentagon: LFEHT=21,
the sum of these areas is 144 = 12*12;
p(3*n+1) = p(3*n+2) = 0, as the areas of all pieces are multiples of 3;
a(n) = 0 for n > 48;
a(n) <= a(24)=844 and a(24 - k) = a(24 + k), 0 < k <= 24;
A165272 and A165273 give first differences and partial sums.
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LINKS
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Wikipedia, Ostomachion
Bibliotheca Augustana, Ostomachion
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EXAMPLE
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p(3) = a(1) = #{NCO, KHT} = 2;
p(6) = a(2) = #{EFQ, GCQ, BKH, ZLF, NCO+KHT} = 5;
p(9) = a(3) = #{GNC, EFQ+NCO, EFQ+KHT, GCQ+NCO, GCQ+KHT, BKH+NCO, BKH+KHT, ZLF+NCO, ZLF+KHT} = 9;
p(12) = a(4) = #{EQG, ALZ, ABM, BML, FQCZ, GNC+NCO, GNC+KHT, EFQ+GCQ, EFQ+BKH, EFQ+ZLF, EFQ+NCO+KHT, GCQ+BKH, GCQ+ZLF, GCQ+NCO+KHT, BKH+ZLF, BKH+NCO+KHT, ZLF+NCO+KHT} = 17.
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CROSSREFS
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A008585, A001651.
Sequence in context: A023603 A002797 A062492 this_sequence A139672 A093694 A068006
Adjacent sequences: A165268 A165269 A165270 this_sequence A165272 A165273 A165274
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 13 2009
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