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A165271 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. 2
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..68.

Wikipedia, Ostomachion

Bibliotheca Augustana, Ostomachion

EXAMPLE

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.

CROSSREFS

A008585, A001651.

Sequence in context: A308760 A062492 A268346 * A308827 A139672 A308873

Adjacent sequences:  A165268 A165269 A165270 * A165272 A165273 A165274

KEYWORD

nonn,look

AUTHOR

Reinhard Zumkeller, Sep 13 2009

STATUS

approved

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Last modified April 4 04:02 EDT 2020. Contains 333212 sequences. (Running on oeis4.)